Ok, here's a few methods to delete the icons. Let me know if any worked for you?
1. Refresh the desktop and see if you can now delete them.
2. Boot in safe mode and try deleting them.
3. Go to the desktop folder/s and try deleting from there. The typical path is
C:\Users\UserName\Desktop or
C:\Users\Public\Desktop.
4. Use freeware
Delete Doctor utility to lock and delete them on reboot.
5. If they are leftover icons after un-installing a program, install the program again, delete the desktop icons and then uninstall the program.
6. Open Regedit and navigate to
HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows\CurrentVersion\Explorer\Desktop\NameSpace
Double click on
NameSpace and check inside each of the GUID folders. If you are able to identify the icon by name, delete it. This is esp useful for deleting some un-deletable system icons.
7. Open cmd, use syntax
RD /S /Q “pathname” where:
/S : Delete all files and subfolders in addition to the folder itself. Use this to remove an entire folder tree.
/Q : Quiet – do not display YN confirmation
Use these keys depending on your need.