Hi,
It sounds like you have a .htaccess file within the directory that also contains the login page and other files for your webmail script.
Have a look in the dir for a .htaccess file and either amend it, or rename it to something like access.txt
That should stop the users being prompted by the pop-up box for a login, but make sure it doesn't affect the actual working of the script (it may contain some other variables like a rewrite rule - if it does, then simply remove the access parts of the file and leave in the rewrite conditions)
HTH
Jonathen