In the scene from Kill Bill where Hanzo Hattori writes "Bill" on the glass pane, why did Beatrix feel so compelled to erase it, and erase it afterwards? She could also have ignored it, because it would go away without a trace after some time.
This appears to be a special reference/credit for an older movie featuring a very similar scene:
The similarities between the scene in Kill Bill and the scene in The Story of Adele H. are too many to make it just a coincidence, in my opinion.
Quick look around reveals that Tarantino is a big fan of easter eggs and hidden references in his movies, e.g. this post. Hence, it makes it even more likely the only reason the scene was shot this way is to be used as such a hidden reference.