Shows and movies purchased via iTunes, which show up under "My Library" when using AppleTV+ app on a Roku, FireTV, etc. are not available via AppleTV+ web site, and are therefore not downloadable via StreamFab.
The AppleTV+ web site is for AppleTV+ content only. See -> https://discussions.apple.com/thread/253584622 And StreamFab can only download from the AppleTV+ web site.
If its purchased, and viewable in iTunes, yes, DVDFab DRM Remover for Apple *MIGHT* work... however, it was discontinued some time ago because it doesn't work to remove DRM from titles that require newer iTunes versions. *IF* the show/movie on iTunes you wish to use can be played back with iTunes 12.9.0.167, then DRM Remover *MIGHT* still work.. BUT if its a newer title, DRM Remover will not. And with being discontinued, don't expect any help from FAB support.
NOTE DRM Remover still works for iTunes Music/Apple Music for me.
If you are looking at downloading purchased movies from iTunes, then your best option is hope they are from studies that support MoviesAnywhere, and link your iTunes, MoviesAnywhere and Amazon Prime accounts, and download from Amazon. Of course not all studios participate in MoviesAnywhere (like Paramount and Lionsgate being two of the biggest who don't), so not all movies will transfer/sync.
If its TV Shows, or a non-MoviesAnywhere eligible movie, then your only option is screen recording, however AppleTV+ web has a limited resolution, so expect 360p or 480p at best. (this is also the reason StreamFab only offers low resolution downloads on AppleTV+)