Hi HomerJ,
Try the following as I just tested it on my system and it worked. Keep in mind I have full permissions and rights and am an administrator on my system so if you are limited you may have to get access accelerated or an IT admin to clear the registry keys for you and your users.
Do the following:
1) In the run bar next ti the start button type "regedit" and hit enter (minus the quotes of course)
2) The registry editor should open (if you have the rights and permissions to do so)
3) Navigate to the following key: HKEY_CURRENT_USERSoftwareMercury InteractiveQuality Center
4) on the right you should see a listing of the keys under the Quality Center folder
5) all the URLs that appear in your drop down should be there
6) Select one of the keys that contain the URL to be deleted
7) Right click on the key and select delete
8) Repeat step 7 for all URLs to be deleted
9) Relaunch the ALM Explorer and the undesired URLs should be gone.