I see what you mean by the distractions in the reflections. I wouldn’t remove all reflections, but like @frazer-family was say, it would look better editing out the splotch of black that is the photographer. I did this edit in PS, using a light gray color layer masked so it would cover only the photographer, and then cloned around to make the rest of the ring look less splotched looking. If you wanted to, you could literally redo the entire ring with a gradient, but that would probably look a bit fake unless it was done perfectly.
