Really? Exactly which PUA recommends thanking women more as a way to pick up women? That seems out of character.

Quite a few PUA schools advise ignoring behavior you don't like, and rewarding behavior you do like, as well as ensuring that you aren't inadvertently sending out a lot of positive reinforcement just because someone is attractive.

True, "thank you" is not generally a recommended form of reinforcement; non-verbal reinforcements like smiles, nods, touch, laughter, looking interested, turning towards the person, etc. are more generally recommended. Occasionally, a certain old story is cited: the one about the professor whose class conditioned him to stop pacing back and forth by looking interested only when he was in the middle of the room.