While it won't be perfect, a couple passes of Brownell's Oxpho Blue rubbed into the shiny area with a small pad of 0000 steel wool will cover it and tone it down, leaving a gray-black color.
You are already aware that getting too exuberant could damage the surrounding Damascus finish. But if you work carefully, and don't get too far beyond the shiny damaged areas, the steel wool will feather in the coloration, and not obscure the surrounding Damascus pattern. It would be best to start with the spot hidden under the forend wood, or better yet, practice on a set of junk Damascus tubes. Pour the Oxpho Blue into a small bottle cap or something so you don't contaminate the whole bottle with a dirty pad. For the amount you need, try to find someone who has a bottle, and could give you about half a teaspoon or less. It is very tough stuff, and won't rub off like a Sharpie or other cold blue.
