That's enough of a formal invitation! He smiles again in return, a real one this time and not just in amusement at the Library, and strolls over. "I abandon my knowledge of the hour at the door, here; but I shall trust to your word and your judgement."

He nods at the headphones. "What have you found to listen to?" That's one of the listening devices, probably! And if it's not, she can laugh at him for being ignorant, and that'll be all right.