From the way Regulus tenses momentarily at the touch, it's clear he isn't entirely comfortable with it, but from the little nod he gives Harry, it's also clear that he does understand and appreciate the sentiment. He doesn't say anything more for a couple of moments, looking over at Harry as they walk.

"I have a bathtub in my flat," he says, a little uncertainly, at last. "You may as well use it. It's rather a waste of space, otherwise." One of the fringe benefits of being selectively incorporeal, it turns out, is that bathing isn't particularly necessary - or, actually, particularly easy. "And I imagine you'll need somewhere to stay tonight."