I don't know when exactly the policy started, but were taught, beginning in USMC boot camp and reiterated throughout my time, that war trophies are strictly prohibited under article 103 of the UCMJ - and the bringing or mailing back of firearms under any circumstances is a serious crime.

Nonetheless, claiming abandoned US property wasn't so strictly enforced. Grenade boxes, ammo cans, empty shells packed full of trinkets, rocks, and other benign items of novelty. I heard of a guy who mailed home the broken steering wheel of a vehicle blown up by IED with him inside. I have a couple wooden grenade boxes in the attic packed full of silly stuff - uniform items from friends I made in other NATO forces in Kosovo, Sadaam dinars offered by civilians for cigarettes, and other such small things.
Sorry, Kosovo, Iraq, and other modern places weren't quite as interesting in comparison to previous times.