Removing a chromakey background

I know how to remove a background using magnetic lasso and also with the eraser tool. The problem in this shot is the green is reflecting a tiny bit back onto the dog. Is there a way to remove a background by the color?

Thanks in advance for any suggestions.

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After removing the background, you can try to go into the saturation and desaturate some in the green channel. You may have to select where the green is if there is an adverse effect on other parts of the dog.

Especially the parts hidden by the background!