Surprisingly, Natsu backed down from his attack by himself, albeit with bit of "convincing" here and there.
Unfortunately, I still dislike his character a lot, and I still believe that Gemma acted without malice in that incident. So yeah. I'm having a hard time changing my view of this event as anything more than breaking-and-entering. The best thing he can do to crumble the guild's philosophy internally would be to beat them in the tournament.
On another note, is there some rule in the tournament battles that says competitors can only fight opponents of the same gender? I'm asking because that's exactly how it has been so far.