I'm tidying up an old stock for a friend and around the top of the grip, where the back of action sits in the wood, theres quite a lot of staining. I think this is because this is an area where the grain is open and its let oil or sweat soak in over the years.

Does anyone know if this is likely to cause any issues when I oil the stock? It's back to original wood, all the old finish is gone and it looks really tidy apart from some visible staining in this area. Everytime I've passed over this area its clogged the sandpaper up so obviously quite well soaked over the years. I dont want to try and rub it out as that's going to alter the shape of the stock. Getting ready for a good rub down with fine wool and thought I'd ask advice on here before I starting applying coats of oil only to find it's going to look horrible in that area.