Most likely there's a stuck instance of the GUI running in the background.
If you go into Task Manager, then the Processes tab, look for "RedGate.SQLBackup.UI.exe". If there's one there, try killing the process with the "End Task" button.
Once it's gone, you should be able to start up the GUI.
If the problem persists after doing that, then your local cache files may be corrupt, so repeat the above to kill any existing processes, then go into "c:\\users\\<your username>\\appdata" and then delete the files in:
local\\red gate\\sql backup
roaming\\red gate\\sql backup
When you next start the GUI it should be ok, but you may need to re-add your servers to the list.