Most of the little nik-naks dudes picked up were shipped home to avoid customs. I know people are buying/shipping C&R rifles back, but nobody around me did. We traded patches, but we were not particularly interested in anyone's uniforms around us
Most of the weapons and parts we found that weren't destroyed were given directly to the ANA handlers and handed out. We bounced around a lot to different fairly large fobs, so we didn't really have a lot of leeway for a treasure/trinket collection.
Customs would kick back any sort of UXO, brass, anything organic, a certain amount of pirated movies, opened meds, anything "gun part" looking that wasn't attached to your weapon. It would not have been difficult to slip tiny things past customs, but it wasn't worth the risk when you could just ship it, no questions asked.
We brought an 82mm baseplate back by simply sharpy marking a "serial" on the bottom, marking it as inventory, and putting it in the conex. Everyone in the section signed it, and It's a pretty cool piece for the old office.