How to remove reflections from an image

[Krikor]

I tried as follows:
I created a new layer and filled it with gray #343434, multiply mode (Maybe linear burn was another option);
With fuzzy Select Tool, I selected the bright part of the image;
On the new layer (in gray) I created a selection mask.
I adjusted the opacity of this mask and applied a blur to the mask to lessen the effect.
   
I think those were the steps.