He sees her in the company of his own "family circle" for the first time (by his own admission, the only people in the world he does not "think meanly" of), and she's getting along just fine. Col F pays her so much attention he has to jokingly warn her that he can't make her an offer, and Lady C is later sorry to see her go and insists she stay longer.
He's flummoxed. How did she come about? Not an easy question to ask of a woman whom you hugely admire even though you still aren't sure you should.
Ultimately, I think D is trying to compliment her ("Wow, Elizabeth, you're nothing like your mother! You're welcome.") and dig for info at the same time without seeming to, but he is so guarded (from indecision and general social awkwardness) it is all coming off very strange.
