I agree that her expertise is limited to "what you SHOULDN'T do", but.... Dora is his ex- and Tai is his boss; they're the two people in the world over whom Marten holds NO influence or authority whatsoever. I mean, yeah, he might've stayed to find out if only to be polite, but his relationship with Claire *is* more important to him than their relationship with each other. It's not like they needed his supervision or anything, and Faye's desire for gossip similarly isn't his priority.
I just hope that Marten has the good sense to not spring such deep and life-affirming questions on Claire the moment that she gets home - brain-friend and exhausted - from her exam. That won't end well.