You can carefully use the sharp edge of an exacto blade to scrape the carbon off the piston dome. Don't be concerned about getting 100% of the discoloration and end up gouging the piston. Just go slow. What you see is absolutely normal for Lawnboy.

The cylinder is tougher and you need the right tools for the job. Do not use sharp edged tools for this location. The cylinder has a hard metal liner. The top of the cylinder is often soft alloy. You most certainly do not want to put grooves or divots in anything. Pe Reivers suggests a piece of broken glass and it makes sense in a way. Ball hones and soft brass conical brushes also do the trick.

Any way you go about it, before you do anything else stuff some clean cloths around the piston rod where it enters the case. That both protects the rod and keeps the crap out of the case. Whe you reassemble the engine apply a coat of whatever oil you will be running to the piston and cylinder. Not dripping but wet enough to lubricate for that first start up. Otherwise you will be starting a dry engine and that's not good at all.