I just ran into this annoying problem as well. I have a clean desktop (icon free) and like it this way. If you do to, this solution should work for you.
Go into control panel, appearance and personalization, personalization. Click on change desktop icons on the left. Mine were all unchecked, so I turned them all back on and hit apply. It made the recent place icon disappear. I then unchecked all the boxes again and hit apply. Voila! Clean desktop again.