I don't think BIRD DOG used any mercenary forces - all the regiments I can find listed on Sarna that participated were House units. BULLDOG involved at least a number of mercenary commands though - the Crater Cobras, Kell Hounds, and two regiments from the Northwind Highlanders, I think. With the exception of the Kell Hounds, none of those units really feature in Field Manual: Mercenaries (3059) or Field Manual: Mercenaries (Revised), and the Kell Hounds have a pretty minimal level of Clan tech in the rules for them in FMM(R) - they can swap out two weapons per lance for Clantech stuff.
It sounds like the question is moot for BIRD DOG as that only involved 9 ad hoc companies of troops; if you're having mercenaries involved in BIRD DOG, then they're in some pretty rarified company, and could probably get away with pretty generous terms, but wouldn't have the pilots on the ground to take much stuff away. Given that Clantech stuff seems to have been a pretty minor thing in mercenary units pre-Jihad, I'd suggest that the Great Houses arranged to keep as much of the Clan salvage as they could from BULLDOG, but that depending on the House involved, the terms for getting it would be of varying levels of generosity - and given the traditional saw about how difficult Clantech is for mercenary units to maintain in the first place, most were probably pretty comfortable selling on anything more complex than simple weapon systems.