Create another layer. Position it underneath the layer with those white-lined boxes. Take the erase tool, set opacity to 50%, set your brush size to like 200 pixils, and go over your image. This will make the boxes partially transparent. Now, select your other layer and do whatever you want to it. You will be able to paint on the white surface only and still see the boxes.

As of now, I can't give you a better explaination than that since my Maya computer just overheated.