Can't Delete Background Image - 188.8.131.52 user found helpful
This is a current limitation of the theme customizable styles. There is a workaround though.
Use a 1px transparent PNG file as the default image in the theme customizable style. Using the transparent PNG, this will make the default state transparent (using only 150 bytes or so), allowing new background images to be selected and removed by clearing them.
There is an active issue for this. I recommend commenting if you would like for this feature to be added.
"Add ability to select "no image" in style presets for images #1929"