In grainy black and white, they could see the enemy manning the barricades and a guard shack. As they prepared to launch their attack, the pilots noticed a potential complication: Two cars approached the checkpoint and stopped. The drivers appeared to be talking with Islamic State fighters.

Other cars moved through the checkpoint, but these two vehicles remained on the side of the road. Five minutes passed. Then 10. Nearly 40 minutes had gone by and the two vehicles still had not moved.

Running low on fuel and time, the pilots concluded that the people in the cars were allied with the militants and asked for permission to strike. After a brief discussion with their headquarters in Qatar, they got their reply: “You’re cleared to execute.”

This was one version of what war had become in the last years of the Obama administration: The pilots made two strafing runs over the checkpoint, their machine guns cutting through the two cars. Then they unleashed a 500-pound satellite-guided bomb that engulfed the area in dust, fire and deadly shrapnel.

As they returned to their base, the pilots offered an in-flight assessment of their mission: guard shack flattened, two vehicles destroyed and four enemy fighters dead. “There are no apparent civilian or other collateral concerns,” their report concluded.

The first signthat they had made a horrible mistakecame in the form of an email, sent two weeks after the March 2015 airstrike, to an Iraqi citizen working at the U.S. Embassy in Baghdad.

“I am Raja’a Zidan al-Ekabee . . . ” the email began.

‘We anguish over this’

President Obama came to office promising to end the United States’ long and costly wars in Iraq and Afghanistan. Instead of sending tens of thousands of ground troops to distant battlefields, he has increasingly relied on aerial drones, attack planes and small numbers of Special Operations forces. Instead of using the military to try to rebuild broken societies as his predecessor did, Obama has directed his commanders to focus on killing the enemy.

But as the checkpoint bombing outside Mosul demonstrates, even such narrowly defined missions can be morally fraught. Even the most surgical of strikes can carry unintended and deadly consequences.

In his final months as president, Obama has touted his toughness even as he has worried openly about the toll American airstrikes take on innocent civilians. Earlier this month in an Air Force Academy commencement speech, he rattled off the names of nine al-Qaeda and Islamic State leaders who were killed or captured on his watch to cheers from the cadets and the crowd.

A few weeks earlier, in response to a question from a University of Chicago law student about the morality of the U.S. drone campaign, the president reflected on the “tragedy of war” and the need to protect innocent lives.

“We anguish over this in a very serious way,” he said.

The White House is on the verge of releasing a long-delayed accounting of how many militants and civilians it has killed, primarily with drones, in countries where the United States is not at war. The list will include airstrikes in countries such as Libya, Pakistan, Somalia and Yemen.

It will not include deaths in Iraq or Syria. Nor is it likely to mollify critics who say that Obama’s largely defensive, low-American-casualty approach puts too many civilians at risk and too often feeds resentment that benefits U.S. enemies. The report will mean little to Iraqis and Syrians in places such as Mosul, Ramadi and Raqqa, where the tragic consequences of American mistakes are often easily ignored and American precision bombs sometimes do not seem very surgical or precise.

In nearly two years of fighting in Iraq and Syria, U.S. officials say they have killed as many as 20,000 Islamic State fighters and caused only 41 civilian deaths. Military analysts and human rights activists said those figures are absurd. “They don’t pass the straight-face test,” said retired Col. Christopher Kolenda, who led troops in Afghanistan and served as a senior adviser to U.S. commanders there. He recently completed a study on civilian casualties for the George Soros-funded Open Society Foundations.

Since the U.S. military began bombing in August 2014, it has not made a single condolence payment in Iraq or Syria, military officials said. The burden is on Iraqis and Syrians to seek compensation for American mistakes, but for those who lost relatives, there is often no clear way to even lodge a complaint.

Ekabee’s email was a desperate attempt to catch the attention of the U.S. military’s vast bureaucracy.She wanted the Americans to know that their pilots had destroyed her car and killed multiple civilians.

The emailpassed from the U.S. Embassy staff to the U.S. military command in Baghdad and then on to investigators in Qatar. In it, Ekabee described fleeing her home in Mosul and paying a driver to smuggle out the car she had left behind.

Her 2011 Kia Sorento, she wrote, was stopped at an Islamic State checkpoint near the Iraqi village of Hatra when a “missile of the international air forces struck the checkpoint.”

Inside the Kia, along with the driver, were three women and two children. The car was traveling with a GMC Suburban when the bombs and bullets hit, causing both vehicles and the people inside them to “burn entirely,” she said.

Ekabee had planned to sell the Kia to support her six children.She did not know the people the driver had brought with him on the trip.

“Please kindly approve the request of compensation for my car because I have already lost my house, which was seized and looted by Daesh,” she continued using the Arabic slang for the Islamic State. “This car was all I have.” In a later email, she attached photos that her relatives in Mosul had taken of the Kia, riddled with bullet holes and burned beyond recognition.

‘Communications error’

In Qatar, American investigators replayed the footage from Hatra on a large, high-definition debriefing screen at their headquarters. They watched on the screen as the pilots made their first pass, blasting the checkpoint, the Kia and the GMC with machine gun fire.

Six seconds before the pilots made their final machine gun pass, the investigators spotted three people rushing out of the burning GMC and one person fleeing the Kia. It was hard to tell whether they were men, women or children.

Only by pausing the image and measuring the shadow height of the figures did the investigators determine that one of the human-shaped forms was probably a child. “The small signature is visible for approximately one second,” the investigators wrote in their report. At that point, the machine gun rounds, which took three to four seconds to reach their target, were already in the air.

The 500-pound bomb followed a few seconds later. Through a cloud of smoke and flames, the investigators noticed one person moving in the back of the burning Kia.

The report identified a “communications error” during the hurried conversations between the pilots and their headquarters before the strike, but the Air Force general overseeing the inquiry concluded that the mistake “did not affect the final outcome” or cause the civilian deaths. No one was punished as a result of the findings, but investigators did make one notable change to the final casualty count. The attack at the Hatra checkpoint had killed the four enemy fighters initially identified by the pilots and the four civilians who had fled the cars, they concluded.

‘The lives of innocents are cheap’

Ekabee first learned that something had gone wrong when she tried to call the driver whom she had paid $1,500 to smuggle her car into Baghdad. Negotiating the Islamic State checkpoints around Mosul was a dangerous business.

“Only the drivers could organize it,” Ekabee said. “Normal people couldn’t. You needed agreement from the authorities in Mosul.”

The driver made the trip out of Mosul as often as two times a week, delivering cars and ferrying fleeing residents out of the city. He told Ekabee that he had developed his own survival strategy. He never carried young men.

“Just women, children and families,” Ekabee said. If possible, he brought along an elderly woman. The Islamic State fighters would let people through if they looked old or sick or if they needed medical attention, he told Ekabee.

He often traveled with other cars and this time was making the journey with a black GMC Suburban, driven by a friend. On this trip he also was carrying close relatives.

“I think this time his family decided to flee permanently,” Ekabee said.

The trip to Baghdad, where one of Ekabee’s relatives was waiting for the car, was meant to take a day. The following morning, there was still no word from the driver.

When Ekabee tried to call his cellphone, an automated message told her that it had been turned off. Ekabee, who has been living in the Kurdish-controlled city of Duhok since fleeing Mosul in 2014, asked her relatives in the city to visit the driver’s home.

There, they found funeral tents for the driver, his grandmother, aunt, sister and her two children. The six had been killed by the American airstrike, their bodies so mangled by fire and the blasts that their remains had to be carried away in shopping bags, Ekabee’s relatives said.

Images of the flattened checkpoint and mangled cars played on Iraqi television.

A provincial government official in northern Iraq told Ekabee that the family of a lieutenant colonel with the Iraqi police had been burned alive in the GMC Suburban.

“What happened to me, you can’t even imagine,” the colonel said last month in interview with The Washington Post. He said his 9-year-old daughter; two sons, ages 10 and 16; his wife; and the driver were killed in the attack. He spoke on the condition of anonymity because he still has family trapped in Mosul.

After the strike, his commander, fearing that the colonel might commit suicide, took away his weapons and ordered two policemen to stay with him. “I never received the bodies,” the colonel said. “The people of Mosul buried them.”

Ekabee was instructed by a lawyer at the U.S. Embassy in Baghdad to take the pictures of her burned Kia and her ownership documents to the U.S. consulate in Erbil. “They didn’t ask me for any details about the families,” she said.

More than a year passed with no reply from the U.S. military. A few days after The Post asked about Ekabee, she was informed via email that “a thorough investigation” had determined that the U.S. military had blown up her car.

But the U.S. military was not obligated to compensate her for the loss because it was destroyed in “combat activity,” the email stated.

Col. Patrick Ryder, a spokesman for U.S. Central Command, said in an interview that the military could make condolence payments to relatives of the civilians killed at the checkpoint, but that no one has stepped forward to request compensation.

“We don’t know the identities of the deceased at this point,” he said.

If U.S. military officials had called Ekabee, she could have pointed them to the police lieutenant colonel, who said he never made a formal complaint with American officials. “I only complained to God,” he said.

Ekabee could have helped them reach the driver’s relatives.

If they had called her, U.S. military officials also could have learned that their investigation of the Hatra attack, which concluded that there were four civilian deaths, was incorrect. According to Ekabee, the colonel and government officials in Nineveh province, at least 11 civilians were killed — more than double the number in the U.S. report.

“This email means that the lives of innocents are cheap,” Ekabee said, “and that they don’t want to be responsible for their mistakes.”

Reporting — and paying for — casualties

The Hatra strike also points to another problem: Nearly two years into the U.S. bombing campaign, there are still no real channels for Iraqis and Syrians to seek redress when their civilian relatives are accidentally killed or injured in American attacks.

At the height of the U.S. occupation of Iraq, someone like Ekabee could have filed a complaint at one of the hundreds of combat outposts scattered around Iraq. In Afghanistan, where it’s harder to travel, the military established a Dari and Pashto-language website and text messaging service to help Afghans alert them to civilian deaths.

In both war zones, preventing mistakes and making condolence payments were once considered not only a moral imperative, but a critical piece of a broader American strategy aimed at rebuilding fractured societies and winning the support of the population. To that end, the United States paid out hundreds of millions of dollars to Iraqis and Afghans who suffered losses.

The commanders’ focus also helped drive down the civilian death toll. In 2009, the United States was causing one civilian death for every six airstrikes, according to U.N. data and a recently released report on civilian casualties by the Open Society Foundations. By 2014, the rate had decreased to one civilian death for every 11 airstrikes, according to the United Nations.

Because so few American troops are operating in Iraq and Syria, U.S. military officials say it is difficult to conduct thorough civilian casualty investigations. So far the military said it has looked into 178 allegations of civilian deaths and, relying almost exclusively on gun-camera video for confirmation, found 129 of them not to be credible. The remaining 49 were found either to be credible or are still being investigated. “We don’t have the traditional means of doing interviews, knocking on doors, forensics testing — the kinds of things you would do,” Ryder said.

As a result, many mistakes in Iraq and Syria are never even recognized as such.

Massoud Hameed said his brother, sister-in-law and their three children were killed on Nov. 24 when an airstrike hit their home near Bashiqa, a small village in northern Iraq. He complained to his parliamentarian, who said he contacted the U.S. Embassy.

“I demanded compensation,” said Salim Jumah Mohammed, the lawmaker. “I demanded the coalition should not bomb civilians.”

The deaths were reported in the Iraqi media and logged by Airwars, an organization that tracks civilian casualties in Iraq and Syria. The U.S. military confirmed that it carried out a strike that day in Bashiqa, but said it has not received any complaint that civilians were killed.

Obama has touted his approach in Iraq and Syria as a more humane, efficient and effective alternative to large-scale occupations of the George W. Bush administration. Such military operations cause more deaths among U.S. forces and civilians, Obama has said.

“Our military engagement as a general matter is far more focused on disrupting and defeating a specific terrorist network and therefore inflicts far less damage than invasions and occupations,” said Ben Rhodes, a deputy national security adviser.

Since the Hatra strike last year, the U.S. military has increased the intensity of its bombing campaign with the goal of cracking the Islamic State from the air. Until recently, U.S. commanders in Iraq had to get approval from U.S. Central Command in Tampa if an airstrike was considered likely to produce civilian deaths.

“Now we don’t,” said Col. Steve Warren, a U.S. military spokesman in Iraq. The new threshold of potential civilian deaths that can be authorized from Baghdad is classified. “It’s gradually increased,” Warren said.

U.S. attack planes and drones have begun pounding the Islamic State’s oil infrastructure, cash storage sites and supply lines. “We want to hit them every time they come into the open,” said a senior administration official who spoke on the condition of anonymity to discuss military plans. “We want to make it hard for them to use the roads or rivers to move fighters, weapons or money.”

The approach is producing battlefield gains. The Islamic State has lost 45 percent of the territory it once held in Iraq and 20 percent in Syria, according to the White House. Less clear is whether the military success will make it any easier to address the sectarian grievances and governance problems that have fueled the chaos in the country since the U.S.-led invasion in 2003.

For the Obama administration and the U.S. military, the big question is: What will be left behind after the United States stops bombing?

‘America’s been sleeping’

Ekabee and her family offer one answer. She, her husband and children are crammed into a small, bare apartment in a Duhok neighborhood known as “Nineveh City” for the thousands of displaced Iraqis who have fled there from Mosul and surrounding Nineveh province.

She worries that the driver’s relatives blame her for their loss and seek retribution. “I was afraid that they would pray for God to take revenge against me,” she said. “The driver is the only son in his family and he has four sisters. He’s doing his job, smuggling cars, in order to provide food for his family.”

She wonders what has become of her six-bedroom house and her garden in Mosul. “If I try to describe it, I’ll cry,” she said.

Initially, the Islamic State used the house as a jail. More recently, her relatives told her it was serving as a guest quarters for foreign women who had come to Iraq to marry Islamic State fighters.

Before her Kia was destroyed, Ekabee planned to sell it and use the money to support her children and send her eldest son to school. “This car was the only hope I had to provide a decent life for my children,” she said. “Now we have no hope. We lost our city, our house and the only money we had.”

Her husband insists that the United States isn’t doing enough to drive the Islamic State from Mosul. “America’s been sleeping,” he said. “They’ve done nothing. The coalition with all their power can get them out. Half the people are willing to die just to liberate Mosul. They don’t have a life. They might as well be dead.”

Ekabee is more resigned than angry, convinced that the American military and Obama’s cure for her city is as bad as its current disease. She has seen the pictures of Ramadi after its liberation earlier this year by U.S. air power and Iraqi troops. Today that city is essentially uninhabitable — little more than rubble and leftover Islamic State land mines.

“We expect the same destruction in Mosul we’ve seen in Ramadi,” she said. “But this is our fate. What can we do?”

Morris reported from Duhok and Baghdad. Mustafa Salim in Baghdad contributed to this report.