Remove “Connect to Internet” Icon

Have a W2K domain with new W2K Pro workstation. Do not use profiles. How can I remove the “Connect to the Internet” icon when a domain user logs on to the new workstation for the first time? We don’t need the icon, each user is able to connect to the internet through our proxy server by double clicking the IE icon. Have tried removing it from all users desktop, but it appears for each new user.

Any help appreciated.