Can't Delete Background Image - 184.108.40.206 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"
1. Navigate to the background setting that you are attempting to remove. Go ahead and click the "choose new file" button.
2. Select any image, does not matter which, to be set as a new background. **Important: DO NOT HIT SAVE, or you will need to start back at step 1.
3. If the background setting pop-up menu has dissapeared, just click back into the background you just changed. Now it will show a cued-up preview thumbnail of the image you just selected from your files. Click the blue box (see screenshot attached) that the thumbnail is nested in and it will give you a new menu of options to choose from including "Clear".
I hope this helps!