Jack... isn't quite sure why a hint is being made, but he thinks he gets it. Though he's not sure why Sinclair can't just say 'yo fuck off for a bit would you' if that's what he's getting at.

People in Rapture are so... unnecessarily subtle.

He hesitates, trying to figure out if that really was a hint or just an offer. Either way, Sinclair sure seems to think he can handle this, so in the end Jack nods and backtracks into the hopefully well-appointed kitchen.

If Sinclair listens, he'll hear the not so quiet sound of Jack happily going through every drawer and cupboard and garbage can in the place.