The problem with this picture is not so much the reflection, but the fact that the photograph is:
- small (few pixels to work with)
- blurry
- lots of compression artifacts
- poor dynamic range
- poor lighting
That makes it really difficult to come up with a convincing fix with all these limitations.
Personally I never spend my time on images like this, unless there are emotional reasons involved. For example not long ago I made someone really happy who thought one of his most important marriage pictures was for ever destroyed. It took me two hours, but the result and the response of the owner was really worth it.
My advice with this image: if you retouch it, make sure you have two windows open (menu: windows/arrange/new window). Use one window that shows the complete picture, use the other image to work in detail, this to avoid surprises (and there are more than you would expect) after you zoom out again...