With the inevitable "wear and tear"of years of use, piano finishes will develop scratches.
I have noticed on my piano that even where the front of lid is turned back and rests on the opened lid, there is a line of fine scuff marks caused by the vibrations when the piano is played.
Most gloss finishes on newer pianos are polyester and the light scratches from dust or scuffing can easily be buffed away with a brass cleaning product called "Brasso".
I have tried it and was delighted with the result. It was recommended by the local Steinway agent. However, I would first advise that you try this method on an inconspicuous part of the piano. Make sure that your cloth is very soft and scrupulously clean as you must rub quite vigorously. Use a circular motion.
I do not know if this would work effectively on a satin finish.
Good luck.
Robert.