Here is a very interesting four-part article about the Hesse jewels robbery. It was published last year on the website of the National WWII Museum.
This 2015 New York Times article reports on other thefts by members of the U.S. military: https://www.nytimes.com/2015/05/06/arts/design/returning-the-spoils-of-world-war-ii-taken-by-our-side.html
Quotes: 'Though stories of art looting during World War II invariably focus on Nazi plunder, German and American officials say thousands of works, among them masterpieces by Dürer, Cranach and Hals, crossed the Atlantic in footlockers and mail parcels in the 1940s. Very few have trickled back...
The thefts from German castles and storage vaults in no way match the scale of Nazi looting, and were undertaken by men who had witnessed the bloody toll of German aggression. But few suggest American soldiers were confused about the rules of war. Gen. Dwight D. Eisenhower had issued strict directives forbidding such thefts.
“Yes, they were suffering and losing buddies,” said Robert M. Edsel, chairman of the board of the [Monuments Men] foundation, which chronicles and promotes the return of art stolen during World War II. “But they knew what they did was wrong.”'
Was it only Hesse that seemed to have experienced looting of royal items by American soldiers?