How to Clean a Kigurumi Mask
External Cleaning
Generally you want to be gentle with your mask, most marks can usually be removed with a 'magic eraser' type sponge dampened with water.
Scratches and minor chips are unfortunately not something that can be so easily wiped away, instead you will often need a small amount of paint to touch up the area. Do not use an oil based paint, instead use an acrylic paint. Paint based pens are an easy option to apply a fine layer of paint to the area. In the instance of scratches, you can usually apply a thin layer, and wipe it away from the surrounding non-scratched area, let it dry, then apply additional thin layers until the scratch is gone. An example of a suitable paint pen are ones such as these Skin Tone based ones from Tooli-Art. The exact shade you need would vary by maker and if the character has a specific skin tone, do experiment with painting a piece of paper or similar first to try to get close before you apply any specific paint to the mask itself.
Internal Cleaning
Padding if removable are generally a good idea to remove and wash, disinfecting wipes or an alcohol based spray can be another solution for those that arent.