I think the idea is that he thought she was confused by what he had said.
"What are they called?" meaning "what are the words for them?" Not "what are their names?" Like he was quizzing her on her English or something.
He was a about to correct her like "no no, I meant what are their names?"
They're not files, it's just leaking other people's conversations through a history bug. Accidentally putting person A's "can you help me write my research paper/IT ticket/script" conversation into person B's chat history.
Super shitty but not an uncommon kind of bug. Often either a nasty caching issue or screwing up identities for people sharing IPs or similar.
It's bad but it's "some programmer makes understandable mistake" bad not "evil company steals private information without consent and sends it to others for profit" kind of bad.