American Special Forces troops were behind a lot of this, as they knew the culture well, and had been studying Iraq for a long time. While cash compensation was not going to make the terrorists or anti-government fighters go away, the payments and kind acts did create Iraqis who were no longer willing to attack Americans, or assist those who did, or became willing to provide information about the bad guys. The compensation effort was worthwhile for the degree to which it made the war easier for the Americans, and harder for the enemy.
Early on, American forces in Iraq adapted their tactics to local customs. For example, in Iraq, paying compensation for a loss is one way a ruler earns the respect, and allegiance, of those he rules. Saddam Hussein was expert at doing this. He was ruthless to his enemies, but would spread money around as gifts if it served his purpose. During the brutal 1980s war with Iran, Saddam kept morale, and loyalty, up by awarding parents of dead soldiers thousands of dollars in cash or goods. Those who remained loyal to him in 1991 also received gifts. Thus, almost from the beginning, American troops in Iraq, especially the Civil Affairs detachments, would arrange to pay compensation to civilians who had suffered loss (property damage, or someone in the family dead or injured) in actions involving American troops. The United States would often provide medical care as well, and some units had a procedure where troops would apologize, through an interpreter, to civilians who had been hurt by the combat actions.