Not sure if this is exactly what you are looking for, but I thought I
would share for the benefit of others that might be looking. I
stumbled upon this while looking for ways to disable the option to
"Set As Desktop Background" when right clicking on a picture that has
been downloaded to the computer. I too was frustrated with the lack
of options, at least through group policy to prevent this from
happening.
However, when I looked more at the existing group policies and what
they did, I realized that it may be possible to fool the system
slightly. I made my adjustments in GP, tested it and it worked! Here
are the details:
In GP I went to User Configuration / Administrative Templates /
Desktop / Active Desktop. There I enabled Active Desktop and enabled
Active Desktop Wallpaper. This may seem a bit counter-intuitive, but
bear with me. When looking at the information on Active Desktop
Wallpaper, it reads in part, "If the specified file is not available
when the user logs on, no wallpaper is displayed. Users cannot
specify alternative wallpaper." So, as I said, I intentionally fooled
the system, by giving it a local path, in my case C:\blah.jpg, to be
used as the wallpaper, knowing that it would not find that file,
resulting in no wallpaper being displayed, as described above.
I really don't think it should be this difficult, there should be an
way to remove that option from the contextual menu across the board,
but alas, I was able to overcome it by being a bit creative.
Enjoy!