In one of FFG previevs they wrote: "Take care to balance your lust for gold against your ambitions for character growth, though, as you discard the trophies that you use to claim a bounty." So, if I have for exaple a Dragon trophy with a strenght of 7 and I claim a bounty from Wanted Posters (7 golds) than I can NOT gain one Strenght counter?

Correct. If you claim a bounty to gain gold, you cannot exchange the Enemy as a trophy!

Ell.