Pedants: He asked if she minded. She responded saying, “Sure thing,” which is an affirmative response, meaning that she did mind.

So... when you analyze language, you can think of an utterance's semantics (what it means "at the dictionary level") and pragmatics (what it means in context.) For example, if you're having dinner, and someone asks "can you pass the salt?" in terms of semantics it's a question, but in terms of pragmatics it's generally a command or request for an action.

Similarly, I'd say Batman's first utterance in terms of pragmatics is a request for permission, which is granted by Catwoman's first utterance.