Icons on desktop wont delete

I have an icon for a dial up connection (it does not use DUN) that was installed from my isp's cd. I can't delete the icon, there is no delete option if i right-click, if i drag it to the recycled bin it just pops back. It just wont delete. It seems to be like the my computer icon.

Any help would be welcomed

Have you tried doing a Find - Files and Folders, done a search for it in here and then tried right clicking and deleting? This just might do the trick.