Yes, in settings, but that's not the subject. You can disable it in your Facebook settings, or if you want to keep it, check your message invitations on Messenger to see if there are any unread messages.
Well, go to the menu, then to "settings," "message previews." To disable it, select: "allow message previews on Facebook," otherwise you can try unchecking the options at the bottom to see if the red dot disappears.