There is currently no easy way to remove custom slide backgrounds from the backgrounds gallery once they have been added in Studio. However, as they are simply stored on your local disk in the app data folder, you can remove them from there and after restarting Studio the will be gone.
To do so:
Open Windows Explorer
Paste the following path in the address bar: %appdata%\QuizXpress\Backgrounds
appdata.png (33.49 KiB) Viewed 1153 times
Hit Enter and you will see all your added backgrounds
Delete the images you no longer need
Restart Studio and verify the images have been removed from the gallery.