I think you might be hitting the issue where someone has saved a favourite into a folder, not necessarily to you personally.
In your screenshot I see the 3rd Fav is shared inside of Purchasing Folder. You might have your name ticked on on that folder in Admin / Folders.
In your Profile, do you have the “Share with Folders” option un-ticked?
If so, you then might not be able to save or mange the items in that folder, therefore the Trash option isn’t available to you.
Mine is set like this:
Whereas a user who cant delete or create favourites in folders would have that option un-ticked I think.
How do things look in your Profiles?
The good thing with this unticked, is people can’t create loads of Favourites in your lovely folders, cluttering them up. But the draw-back, is they don’t have the facility to do exactly that. Hmmm
This profile tweaking is a bit complicated.