Personally, I don’t find the reflection distracting; to the contrary! Wedding rings (like any jewellery) are designed to create reflections! If there were none, the ring would look like it were made of plastic.
On the flip side, though, it is distracting that you can distinguish a photographer in the far left ring (if you look closely.) I’ve often seen pictures of rings taken at a very slightly higher angle, and often off-set, sometimes with one sitting halfway on the other, etc… Maybe it’s to avoid that problem.
I tried (rather fast) cloning (using a half-transparent brush) from either side of the photographer, after partially blurring it out (again, half-transparent brush). Then to avoid a ‘out of focus’ feel, I used a sharpening brush the same way. It’s called convolve in Gimp; here’s an explanation of what it does. There must be a very similar tool(s) in Photoshop. So now you can see a sharp-looking texture (though not very sharp at that resolution), but no photographer.
I don’t like my results, but I’m working rather fast and on a shrunk version. Still, I believe the method has potential.
Hoping this helps,