Just right click on the Desktop logo and then use Delete - it's only a shortcut.
Don't understand your reference to the white Tiscali log behind the IE title bar though...:-(
There's a much easier way to get rid of the branding than going into the registry:
First close down Internet Explorer then click Start and Run. In the Open dialog box type:
(note the space after .exe and comma
(copy and paste will ensure it's error free) - then click OK.
After restarting Internet Explorer the annoying ISP branding should disappear.