I once read a Discworld fanfic where a vampire needs to meet someone in the hotel where they're staying, but the proprietor refuses to invite her in. She gets around it by getting the person she's meeting to invite her into their room directly through the window - since the guest has paid for the room, they have therefore taken (temporary) ownership of it, granting them the ability to offer the invitation. As Gryphon is inviting Remilia into his own room, I would presume something similar is going on here.

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