I guess I can go with the whole small talk business to get her to open up more, but why not use some actual information he's obtained from previous loops? He mentions Hendrix and she immediately starts asking how does he know that - why not use more of those snippets to show her she opened up to him in previous loops? That's an even better way to show he's done this all before.

The scene feels a bit like filler to me (a cardinal sin in screenwriting), and it stands out in what was otherwise a very tightly written script - everything else said and done has a purpose and a reason, but this scene feels slightly out of place. If the scene's purpose is to show how many loops he's done or how he's fishing for information, I think it could have been done in a better way, without the made up middle name and lost brother story.