The background can be removed the following way:
- File > Open the song folder (
screenshot).
- In that folder delete the background and then simply leave the editor. Your map now has no background.
If you only want to remove it from a speficifc difficulty, you can remove do the following:
- Open the respective difficulty in the editor.
- File > Open .osu in notepad
- Locate "[Events]" withing the textile, there you will see
a line like this (highlighted), remove that line and save the textile.
- Leave the in-game editor without saving.