UPDATE: Here is an example of the Delete Key not fixing the problem in Faxanadu:
In the above image, you can see the wall, the windows and the shields are connected to the desk. Also, for some reason, on the left edge of the desk you can see a bottle that's attached to it as well. The Delete button does not separate any of this.
UPDATE 2: Adventures of Lolo.
The bricks and trees won't separate at the top. The bricks won't separate from playable blocks on the bottom.
UPDATE 3: Godzilla.
The mountains that are supposed to be obstacles in the foreground remain part of the background image. Delete doesn't fix this.
On the map screen, Godzilla and Mothra, and the enemy monsters are part of the honeycomb grid and cannot be separated.