There were several fates of military working dogs (MWD) in Vietnam, and unfortunately returning to the USA was the very distant last in that equation. While those utilized during World War II were, as a matter of policy, reintegrated back into civilian live where possible (something I've covered here), a program which was successful in 'demilitarizing' most of the 'war dogs' deployed by the US military, this policy was not carried over to Vietnam, as I mention there as well. To expand somewhat on what I wrote there, MWDs were considered nothing more than military equipment, and as such, there was particular concerns about how to bring them back once the US began to draw down its presence there.

Beginning in 1970, many of the MWDs serving with the US armed forces were simply given to the ARVN, despite the fact that not only was there no real interest in recieving them by the South Vietnamese, but their existing track-record had shown them to be wholly unable to use the animals properly lacking the necessary training or facilities to maintain and deploy them. Back in 1962 several hundred MWDs had been provided by the US Army back in the early '60s, only for many of them to die of malnutrition, and the rest to become neglected and entirely unusable in their called upon role. As for the MWDs turned over in the early '70s, they faced no better prospects with the ARVN either, the handlers suspecting that the Vietnamese slaughted them for food.

For those not turned over, many faced a prospect made less grim only by the relatively humane way they met their end, with the US military unwilling to foot the bill to return them to the US, but willing at least to pay for the cost of euthanasia. Handlers, who had of course formed close bonds with their animals, were violently opposed to the policy, but even requests to cover any associated costs in bringing the animals to the US failed to work. Eventually, public pressure saw a brief change in policy, and some 200 MWDs were quarantined, 120 of which eventually moved to US bases on Okinawa or the mainland US, but it was a one-time deal, and after that, once again the MWDs were either turned over to the ARVN or put down. A small number more 'made it back' through various circumstances, but in total only 204 MWDs are believed to have been repatriated, less than the 350 killed in action, and a fraction of the 4,000 or so who served there.

Thankfully, since Vietnam the policy has changed, being more in line with that originally used in WWII, and retired MWDs get to return to civilian life just like their human counterparts.

Benner, Dana. “No Room on the Chopper: The Plight of the Military Working Dogs in Vietnam.” Vietnam 31, no. 5 (February 1, 2019).

Hesse, Josiah. ​The US Military Euthanized or Abandoned Thousands of Their Own Canine Soldiers at the End of the Vietnam War Vice.com, May 24, 2015