It's hard to tell from the pic because when I click on them they are to big to get any detail,but it looks like the washer has come undone from the collar underneath,originally they were just peened over & maybe somebody worked on the machine in the past & didn't repeen good enough,I would push the lower part back into the upper part so it doesn't have any play but still turns around & just tack weld it in 4 spots.
They call these machine shoe patchers for a reason,that's what they were made for,BUT I know alot of people have done some fantastic sewing on them & as already mentioned,some tape,rubber or grind off the teeh will stop the marking but will also stop the feeding of the leather making you have to push it through.