It's not wierd, a good polishing needs a soft cloth and some kind of polishing wax.
Using natural fibres like cotton and natural grease like fat of a pig with some clay is the traditional way to polish metall...

But polishing always leave behind a clear and regular "polishing track". In case of high glossy polishing this tracks are smaller than 1 µm and very regular.
If the tracks are not regular or bigger than 1 µm the surface is not high glossy, meaning the light is reflected in a more diffuse way.

With DVDs and CDs you must be very carefull to avoid damage to the data tracks, so i strongly recomend to use a special machine for this work, so the tracks of the polishing don't interfer with the data tracks.

CYNIC, n. A blackguard whose faulty vision sees things as they are, not as they ought to be. Hence the custom among the Scythians of plucking out a cynic’s eyes to improve his vision