Hi Dr. Bill, for background, Firefox creates the Old Firefox Data folder on the Mac desktop when it runs the Refresh feature, sometimes called a tune-up. If you don't need the folder at that point, it is safe to delete it. You mentioned that the folder keeps coming back to trash, not the Desktop. As a Windows person, I don't have any tips on why the Mac wastebasket isn't working the way you expect. If you don't get a good answer here, you could try Apple's support forum: https://discussions.apple.com/community/mac (scroll down for different models)