"Oh! No, I didn't mean it like that!" Granted, it had, technically, been an interruption, but Hermione hadn't meant to be rude about it, is what she means. You never tell someone they're interrupting you. Not unless they're Ron. He can stand a bit of rudeness thrown back at him every so often.

She hesitates between going back to her reading and debating whether she should engage the woman in conversation. Seeing what she's doing, though, piques her genuine curiosity. "It is nice, isn't it? Sorry, is that... chess?"

She knows the wizarding world is confused by the notion of chess, calling it instead Wizard's Chess and throwing in some enchanted pieces. Would Thedosian chess have a similar quirk to it?