Get rid of the glare in the photo, you mean?
Careful and likely frustrating Photoshop work.
I would probably go with doing the corrections in Curves and painting them on with the History Brush (in whatever mode looks best) or doing the same thing with a layer mask. The tricky bit is making the transition undetectable.
Bonnie says feather, grab the affected area and dupe it back on top in multiply mode. Which could also be done with a layer mask to make it less frustrating.
Or a combination of those techniques. They all sort of do the same thing.
It looks like a quick Free Transform would be in order to square it up, too.