They imply so much that something happened between them in the past, hinting at it and talking about it...
But never actually revealing what happened. I have to say I'm really curious though, I kind of want to know.
I suppose it works well enough as it is without explicitly revealing it...Maybe a prequel or something?
Sometimes the best story technique is to not give the details. You can accomplish more many times by omitting rather then adding. A sort of Chekhov's Gun essentially, backstory may not necessarily be relevant to the current plot or event.
I like it, you find out enough to understand what's going on but it still makes you curious about them. Gets you invested in their story. Really nice. I don't think it actually needs a prequel, actually I'm more curious about what happens next.
I believe that is something about him being a student at the school she was a nurse in and they had some relationship and that somehow someone caught them. She was forced to retire and he is like this now.