The difficult thing in this kind of retouching is to preserve the natural curve of the surface of the object while removing the reflection. I took a little different approach by creating two duplicate layers above the background layer. The first, Copy 1, is set to Luminosity blend mode. The uppermost layer, Copy 2, is set to Color mode. Make Copy 1 active, choose Image>Adjust>Curves, and bring up the dark end of the curve a lot until the dark tonality of the reflection practically disappears. Add a layer mask to Copy 1, Hide All, and then use a small soft edged brush set to about 50 percent opacity to paint white in the mask in the area of the reflection until the results look reasonable. Then make Copy 2 active, make the foreground color equal to the dark gold color from elsewhere on the ring, and paint in the area of the reflection. Flatten and give the area of the reflection one or two quick hits with the blur tool set to about 40 percent opacity. As Tim Gray says, you need to experiment a little with the settings but this was done quite quickly--it took much longer to type than to do.