A picture frame left a dirty ring on my walls paneling. How do I get rid of it?

I just bought a new house and I saw this outlined octagon ring of dirt on one of the walls. It's a 4 ft by 4ft ring of dirt. I tried some soaps and im afraid to use bleach because it may harm the paneling. Anyone have some remedy?
Update: It's a thick ring, not a filled in octagonal shape. You can tell it was the frame. the inside of the octagon is the same color as the rest of the paneling around the house.
Update 2: It is wood paneling but the face of the paneling was made to look like earth toned wallpaper.
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