Summary:
Custom Wallpaper and Custom Avatar deletion UIs do not delete/remove custom image in Cpanel.  Custom Wallpaper deletion UI is located at User Settings > General > Wallpaper > Custom Wallpaper.  Custom Avatar deletion UI is located at Settings > General > Avater / Custom Avatar.
Here is the Cpanel link I used.  It requires password.  You can contact me for it.
https://admin.google.com/crosprqa3.com/AdminHome?fral=1#ServiceSettings/notab=1&service=chrome+os&subtab=usersettings


STEPS:
pre-condition:
In Cpanel:
1. Ensure User Settings > General > Avatar > Custom Avatar points to a custom Wallpaper image
2. Ensure User Settings > General > Wallpaper > Custom Wallpaper points to a custom Wallpaper image.

procedure:
1. On Cpanel, navigate to User Settings > General > Wallpaper > Custom Wallpaper.
2. Click on Custom Wallpaper deletion UI "X".

results:
Unexpected:  No deletion related button shows up instead "UPLOAD WALLPAPER FILE" button pops up.
Expected:  Some kind of deletion related button pops up.