A simple method to just remove the old dirty top coat would be to use 0000 steel wool and apply a 50/50 mix of linseed oilicon and turpentine. The steel wool will abrade and remove the old top surface coating of linseed oilicon but not strip all layers of oil finish or the wood dye.

Note: A Conservator at a Museum to clean a wood stock would use a soft lint free cloth, a heat lamp and apply a mixture of 50/50 raw linseed oil and turpentine to a small section of the stock at a time. The heat lamp would help sweat and bring the surface contaminates to the surface and be removed with the soft cloth.