Ellen, I tried your suggestion and it didn't work. After reboot the icons are back. I actually tried that last week but I wanted to make sure I didn't have my tongue out or hold my mouth wrong.
I have the following shortcuts on the desktop that I'd like to remove. I like a nice, clean desktop with only the shortcuts to apps I use all the time and if I need any of these apps, I would open them manually. It's more the principle - I should be able to remove these!