Except Bruce definitely saw it, and files it away under 'things to investigate later'. Because he's the goddamned Batman, gosh. The sarcasm he leaves alone, no need to remark on or encourage the attitude, but Derek's assertion that he can look after Stiles is an interesting one. It betrays a remarkable amount of confidence for a boy who looks barely out of his teens himself to have, and the way he handled himself in that fight-- training of some sort, he'd warrant.

Another investigative point.

The order (order, really?) to find a doctor, he summarily ignores as well. "Stick to Feran Street, there's a contingent of undercover police that frequent the cafe there, they're like to step in if there's further trouble."

And just like that, he's gone.