Link makes no claim on anything. Except, perhaps, the right to climb all over anything and everything.

"Your tower. You. A lizard." A lizard which appears to no longer be present - at least not until Link reaches into his pocket, and pulls a three-inch long lizard. Seems Link had managed to collect it just before Tony arrived.

He holds the lizard out towards Tony, to let him get a good look. It wriggles.