As I said before, if the property has been surplused, they would have no legal claim to reposes it. If the property were listed as stolen/lost, there would be an incident report with a board of inquiry- this would be documented-then they would have a right to try and reclaim it The agency can’t suddenly find value in them now if they disposed of them 40 years ago.
If I were in this situation, I would have questions about the chain of custody, lifecycle and decommissioning of these watches. US Government property rules are very strait forward, they don’t bend from one organization to another. There is no difference between a hammer, watch, drill press, camera, etc- accountable property is property and they all follow the same life cycle.
Once property is decommissioned, it can’t be gifted away or taken by anyone in the agency- it either needs to be destroyed (smash it with a hammer, burn barrel, bury it in concrete) or surplussed (traded to a vendor or sent for GSA auction). I cannot opine on the astronauts getting to keep their issued watches or military vets getting to keep theirs- it’s a violation of accountable property law- but obviously exceptions are made (possibly a blind eye) when it comes to consumables and personal issued items (socks, underwear, water bottles- etc).
If the design of the watches were considered classified or sensitive (national security), then there would be a process of disposal or declassification prior to disposal. If said classified materials were taken after decommissioning but prior to disposal (but were not de-classified) like a guy who gets a box of watches in the waste disposal area to smash with a hammer but takes them home instead, then that dude is in deep shit and the property needs to go back for proper disposal- since it has already been decommissioned and thus of no value to the government.
If the first civilian owner took the watch after it was sent for disposal or was gifted the watch by anyone in the agency- then NASA could claim violations of procedures for the disposal- it is still theirs since the disposal wasn’t fulfilled but it’s off inventory.
If I were the new owner of one of these, I would absolutely not just hand it over. It would be locked in a secured location by my lawyer pending an investigation and disclosure from NASA on the chain of custody. Only after they can prove that these watches are still listed as active property or were stolen (police or FBI report would have to have been filed) would I entertain returning it.