They were not allowed to keep their assigned combat weapon. But, for example, we sent 70,000 Marines into Iwo Jima, and 25,000 of those were either wounded or died by the end of the campaign. That's a lot of "unaccounted" for service weapons for bringing an extra one home.
One vet told me that they had big warnings and announcements on every troop ship home that every duffel bag would be searched for contraband. And you could get a lot of nice stuff on the ships for a pack of cigarettes from people who believed that they really tried to search 5000 duffel backs (the story accompanying a near pristine Navy issued 1911 he was selling, picked up on the way back from Okinawa).
F 135 - the right choice