How can I control the list of connections shown when mapping a network drive?

Start the registry editor (regedit.exe)

Move to HKEY_CURRENT_USERSoftwareMicrosoftWindows NTCurrentVersionNetworkPersistent Connections

You will notice in the left pane is a number of string values called a,b,c etc. For the connections you do not want shown, click on the entry and then either press the Del key and say yes to the confirmation or select delete from the edit menu.

Once you have deleted entries you need to update which ones explorer will show by double clicking on order and remove the letters of the entries you deleted

Click OK

Close the registry editor