I'm typing up my post now when I was struck by something. 
Does Tamamo remember past wars here? It was shown she does during Extra (The awkward moment you meet Pieceman and find out he's Tama's Ex) but the moon cell Grail War was fundamentally different than the Heaven's Feel ritual. I was thinking more along the lines of using it for flavoring and humor than lording her experience against Vlad as a tactical advantage.