Hi @F22Simpilot, welcome to the forum!
The automatic tray icon login feature wasn’t added until 2.0.3.7 - and honestly I wouldn’t recommend updating past 2.0.3.5 canary for the moment (and 2.0.3.3 beta is the most stable version for now anyway):
There isn’t a setting to disable the tray icon itself - you just need to remove it from the user’s Startup folder (depending on how you installed it, it might be in the Startup folder for “All Users”).
Of course they could still run it from the Start menu (or direct from the C:\Program Files\Duplicati\ folder) so you may be better off running Duplicati as a service (still with a GUI password). It sounds like the likelihood of your users manually running the tray icon with the --no-hosted-server parameter is pretty low…