Will it invent things about me?

It is built not to. When it does not know, it says so in your voice — "I never told Iphthimé about that." Every memory is marked said (you told it plainly), recovered (it came back under questioning during a Return) or inferred (Selione worked it out), so you always know which you are hearing, and you can correct or delete any of it.

This is also where her name comes from. In the Odyssey, Athena sends a likeness of Iphthimé to comfort her grieving sister Penelope; Penelope asks whether her husband is alive, and the phantom refuses to say — "it is an ill thing to speak words vain as wind." Penelope wakes comforted, having learned nothing. An Echo that invents an answer is worth less than one that admits it has none, and we took the name of something that already knew that. The whole scene.