Your issue is likely a result of Folder Redirection configured on your domain. You're using a roaming profile that copies and replicates/synchronizes your user profile to & from the the server and your client PC when you login and logout of the domain. This can cause files to re-appear if you're deleting them locally instead of on the server.
Login as Administrator to your 2003 Server. Open up the Microsoft Management Console. Press F1 to bring up the HELP screen for the Management Console, Click on the "Search" tab at the top, type Folder Redirection in the search box, then locate the entry "Folder Direction" under the category "Group Policy Management". This has detailed information about folder redirection and how to control it using the Group Policy Management features of Server 2003.
Hope this helps.