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I would just say thanks and move on and talk about something else. There's already some interest if they compliment you.
I don't understand. If there is already some interest, why the hell should he move on?
I don't think there is anything wrong with responding with a compliment, but depending on how you say it, it may sound like you're just returning the favor, which sounds fake.
Make it sincere, go to her eyes, thank her(!), take a good look at her, go back to the eyes and give an appropriate compliment.
I don't really know the details about what you do and what you don't, but remember that looking in her eyes while giving a real compliment is important. And to make the compliment real, have a good look and compliment her on the best thing she has.
Just staying with the eyes works pretty damn well too.
Meaning that you look at her eyes, you thank her, and then look surprised, then just move in a little (and I mean a little) bit closer and act extremely interested. And just tell her she has amazing eyes.
But again if you don't mean it, nobody will be impressed.
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