So in 3DSMax it is sometimes useful to insert a background image usually when you are modelling
something and using the background image as a guide. There is no easy way to remove it. You
can reassign another image or set it to not display the background image, but this can lead to
problems if the file is moved or removed as it is still linked to your max file.

MaxScript to the rescue! You can use the MaxScript Listener(F11) to type in the following to
clear the background filename:

backgroundimagefilename=""

This will clear the entry for the filename. I have noticed that you do need to exit 3DSMax to
fully make the change complete.