Hi
What happens when you right click on it?
Do you get a drop down menu?
Does it have an option to delete the link?
Can you drag the icon around?
If you can't delete it use CCleaner, and look and see if XBox Live Gamercard is one of your startup items.
If so disable it.
You can also use CCleaner to see if it has really been deleted.
See if it is still listed in the programs list.
If none of this helps come back.
Mike