Angry Compliment

The scene plays out at work, where I am already feeling a little discombobulated.

Little old lady: (flatly) You look like Cher.

Me: That's nice. I get Lilly Tomlin a lot too.

Little old lady: No. You look like Cher......only better.

Me: Well, that IS nice, thank you. I wish I had her body.

Little old lady: Cher wishes she looked like you, at her age.

Me: She's had a lot of work done. Even Cher doesn't look like Cher anymore.

Little old lady: I suppose that's true. YOU look like Cher though. (shoves her packages into her cart and exits briskly)

I'm a little conflicted about this compliment.