There is a folder like that under Users someplace, it sounds like it has gotten moved to your desktop somehow which is pretty weird.
It is where the desktop items are really stored. Removing an item from that folder will make it disappear from the desktop.
The normal location is...
C:\Users\"your username"\Desktop
Look and see if there is one in place if not try copying the one on the desktop back to the default location, don't cut and paste.
Then change the name of the folder on the desktop to "Alt Desktop" and see if anything dissapears from the desktop.
If everything dissapears copy the one in Users back to the desktop.
If it is all still there but other stuff dissapears change the name back.
If everything is still normal it should be safe to delete the one on the desktop.
I'm making this up as I go along, but it should work.
Just make sure you don't delete it until you get it so that it is reading from the one in users.
Maybe Neemo knows an easier way to do this.