All of the cats and dogs in my life, including the two I have now, have been adopted from various rescue societies. Every single one of them came with paperwork agreeing to a home visit after adoption.
Not once have I ever actually had a post-adoption visit.
I would tell Diane that the cat’s still settling in and make an appointment for a week or ten days from now if you’re really concerned about her effect on the cat. Let her in for an hour or so on a Saturday morning, and then let her know you’ve got plans/errands/whatever afterwards, and assure her you’ll call her if the cat seems to be having issues.
Then let the adoption agency know she’s having trouble making the break if she calls you again afterwards.