Sounds like its not a 'real' shortcut but you can check. If you open up My Computer and navigate to C:\Documents and Settings\<your user>\Desktop folder, do you see the SCFH listed in there anywhere? Try deleting the shortcut from the folder if it exists.
If it's not there then perhaps try using the built-in 'Clean Desktop' thingy. I don't know how smart it is but you can try it. Go to control panel, find the Display item and open it. You should see a Display Properties window, click on the Desktop tab. Click on the Customize Desktop button, then click on 'Clean Desktop Now'. You will be brought to a wizard that will list the shortcuts on your desktop and when you last used them. Hopefully the SCFH shows up there and you can put a check next to it and clean it up.
If that doesn't work, then its an icon that is placed there through the registry. There is one place I know about (and probably a zillion more that I don't) that can do this, and you have to use the registry editor to get there. You don't have to edit anything, though.
So if you're comfortable using the registry editor, you can try this out: Open up the registry editor (start->run, type: regedit), then open up the HKEY_LOCAL_MACHINE key. Navigate to: Software\Microsoft\Windows\CurrentVersion\Explorer\Desktop\NameSpace
Open that key up and you will see a small list of numbers in brackets, click on each one of them. As you click on each one, in the right pane, you will see text describing what each of those are. One of them should be the Recycle Bin. Hopefully one of them is also the shortcut from *censored*.
