Oil is not a cleaner, especially Tru Oil - that would make a hellacious mess! I don't think I would use anything stronger than a light solution of dish soap with a soft sponge. And then I wouldn't get it very wet. How do you know the wood isn't still sealed from the original finish? Check that out before you do anything else. But be careful because I think you may be getting close to traveling down the road of "if it ain't broke don't fix it.".
