Oil based soap. eg.: Murphy''s Oil Soap.
If that doesnt do it, a single drop of tung oil rubbed into the finish with a bare clean hand (in the direction of the wood grain only) until the oil dries (from the heat of your hand rubbing) and the gloss is restored.
If the ''prints'' still dont remove, .... get *rottenstone* from a
paint store. Thoroughly clean and wet your bare hand. Sprinkle a *small amount* of rottenstone to the wet hand and rub *with* the grain direction until the hand begins to dry and the rotten stone makes a paste (on your hand) .... continue stroking the surface until the level of ultra-gloss is restored. Then clean the rotten stone off with a few drops of tung oil (olive oil if you cant find tung oil) rubbing with a bare hand until the oil dries into the finish ..... will be smooth and super-glossy as original.