Using a desktop microphone and headphones or speakers? If speakers your best bet is dump the speakers. Even if you manage to prevent the feedback you'll just be one of the few speaker users that we will always hear our own voices echo when your mic is keyed not to mention your game.
Whatever you use to mitigate this will likely muddy the quality a bit. I tried using my USB condenser mic before sounds terrible with BG and echo reduction.
I'd do testing outside of ts to try and mitigate the feedback. Play the game sound and then record the mic see if positioning or any deflection will help.