Trust me, I am not the Traitor.
For Orcs there is no other life but WAR!
I can't find a rule that allows to remove the adventure token when Friday did take a wound from it.
The only rule i find is, that adventure tokens get discarded when you resolved a adventure card.
So i would say: No, you do not remove the adventure token. Would be a too easy way to get around These.
I think since Friday doesn't go on adventures then he doesn't remove the token.