How to Clean Solder Stencils?
I have found that the best solution (pardon the pun) is to use Isopropyl Alcohol (IPA). It removes the solder with the least amount of effort. I have had no problems when I have used Isopropyl Alcohol with the no-clean varieties of solder paste.

Methylated Spirits works as well but not as well as Isopropyl Alcohol.

Isopropyl Alcohol will be fine on mylar stencils.

I have found that it is best to use an old rag when cleaning off the solder paste. Tissues etc. catch on the holes and rip, leaving bits of tissue behind in the holes. Steel/wire wool also catches in the holes and pulls and can damage the stencil.