The SettingsLocations.ini file is automatically populated when Toad starts up and is based on the Windows environment variable called "APPDATA". Toad queries this value in order to determine the root location in which to find the SettingsLocations.ini file. This file is then opened to determine the correct locations for each version of Toad that is run.
If you are using Citrix Non-persistent Desktop, which redirects the AppData folder to a server location. The question would be whether the Citrix environment is configured to return that server location when the system environment variable "APPDATA" is called. One way to test this is by jumping to a command prompt and typing "ECHO %APPDATA%" and seeing what's returned. If it's the server folder path, Toad should be looking there for the SettingsLocations.ini file.
If simply has the entries inside this file pointing to incorrect locations, they can update this contents of the file to point to the correct location and it should work going forward (which sounds like it did).