Who Gets Winterfell After This Week's Game of Thrones Episode?

At the moment, Jon isn't allowed to rule Winterfell unless he becomes a legitimized bastard, an offer that he's previously denied. He's also shown disinterest in taking on the position of lord of Winterfell at all, namely due to his status position in the Night's Watch. But because his "watch has ended" and he plays a big role in taking his home back, could he change his mind?