Want to get out. A way out. She wants him to go with her to find a way out of this world, and back into his. DON'T LET HER IN. The vassal thing... a bluff? If he couldn't eat anything here, he'd get hungry, be forced to go back eventually, leading her right to the exit. At least, the eating things part. YOUR NAME IS PRECIOUS- that much, at least, had to have been a real warning. Max can't see how not telling her his name could be playing into her hands.

"I think..." he says, carefully, "I really would like to quiz you about the way the fairy realm works." (To be fair, he actually really would.) "Is this place not safe to talk in? Should we go somewhere we're less likely to be overheard?"