I am torn a bit between saying nothing (which is what everyone else is saying) and giving your ex a "head's up". See, I think most people look at it as if you have 2 choices: say nothing, or say "you're being a jerk and what do I tell her?" But those aren't the only choices.
My husband and I have never been divorced (so take that how you want in terms of my perspective), but he still sometimes can hurt the children's feelings from time to time (and so can I). Even if I don't plan to do anything about it (explain it to the kids, ask him to change anything) I can (and do) still inform him that the kiddo was upset. Then he can do what he feels is best to deal with it. And that is the approach I would probably take here.
Hey, Frank, Chickpea mentioned to me that you woke her up the other night when you came in and she seemed like maybe here feelings were a little hurt. I'm not sure why she told me, but I thought you'd want to know that apparently something about it bothered her. I just told her ____ and left it at that. Just a head's up...
But, if you think he'll take it the wrong way, then don't say anything.
If you think he will recognize that it is strictly informative for HIM about where his daughter's head is at, then go ahead. Your "concern" isn't about what he is doing, but rather that he be aware of your daughter's mental response to it (not that she is right or wrong or that he should change anything).
I mean, if your daughter had a dog her whole life and then one day just before school it got run over by a car when your daughter was in 2nd grade, you'd tell her teacher: Hey-- just a head's up.. if she seems out of sorts today, her dog was run over this morning.
I see these as similar type things... You aren't expecting or trying to prompt any response, but you are giving him information that might be valuable or useful to him. You aren't advocating for anyone. Just giving pertinent information.