Andy,
As MP said, you could get several answers and they could all be correct. IMO, particularly in the ETO, the victors picked up their dead and in some cases, the enemy dead. To my knowledge, nobody, at least in WW II, policed up the brass. The American army left unbelievable quantities of vehicles and fighting equipment on the battle fields everywhere, especially in the pacific.
Dave Harper was one of the world's foremost experts on the pacific theater and he told me that when the Marines conquered an island, we left the equipment including tanks, LVTs, Dukws, artillery and so on where it was. They were re-equipped for the next landing with new equipment. Salvage units maybe came behind, I'm not sure, my impression from Dave was it sat there.
Americans have always been viewed by other cultures as wasteful. After WW II, Europe was covered with tanks and artillery. When my ex-partner, Francois Verlinden, was a kid, he helped his father salvage Shermans and Stuarts from the farming fields of Belgium. His father owned a salvage yard. The armor and trucks were everywhere. The Europeans were still using American and British WW II military trucks for civilian purposes in the 80s. I spent a lot of time in Europe and saw them frequently painted red or blue or black, but, unmistakably, our trucks.
The big diorama I am currently building is a scene of the aftermath of a large battle of land and air forces over a German city. I think as fast moving armies went from victory to victory such as Patton's Third Army, the land behind them was littered with American supplies and equipment.
Bob