I don't think remirror is referring to the song itself, but the dialogue from the scene that occurs afterwards. Watching the scene it actually seems like the chat Ilya and Shirou have when approaching his house doesn't even happen? I can definitely see why now too. Ilya drops a pretty big bombshell in that scene, so including it would possibly distract Shirou from Sakura, which Sudo really wants us to understand how much Shirou is focussing on Sakura at this point, so including that would serve as a distraction.
I definitely see the chat being moved to when Ilya and Shirou are walking back from Einzbern castle in the next movie like remirror suggested though. That seems like a really logical place to put it instead.
At least I hope that's what Sudo does.