MLC is a very good helmet, you did well. The white finish on the helmet looks like the default MLC white. If so, you could try to gently remove the marks and bad surface paint using Goo-Gone. This is a citrus based cleaner that can easily remove the black marks and other paint without removing the white coat.
http://www.walmart.com/ip/Goo-Gone-Pro-Power-Pump-Spray/17300573
If not, you can remove all of the paint using a different citrus based stripper called "Back to nature". It works pretty well and can easily remove ALL of the paint in a about an hour. If you go this route, you'll need to spray it on, let it set, then rinse it off with water. You can repeat as needed to get the paint off, then you'll need to sand and re-finish.
http://www.walmart.com/ip/Back-to-Nature-Hi-Speed-Ready-Strip-32-Ounce-Citrus-Paint-and-Varnish-Remover-Spray/17292210