Old pieces of hand-embroidery that are stained

I have several framed pictures that my aunt hand-embroidered. I would like to remove the pictures and re-frame them.

After dis-assembling one picture, the edges of the material, where the frame was, have dark brown marks (where the picture was set into the frame).

Can this be removed with something? I soaked the picture in regular laundry detergent with Clorox 2 for several hours but it would not budge. I'm afraid to use anything stronger, so as not to cause the colors to run or take the color out of the fabric. Any ideas????