As noted that's not crazing, they are scratches.
Everyone these days loves to use micro-fiber towels for just about everything, myself included but I would give one strong warning:
Store the towel in a plastic bag or other sterile environment between uses because micro-fiber towels are like velcro when it comes to foriegn material laying about. They will cling to and pick up anything they get close too including metal shavings and dirt. If you aren't diligent, the next time you use that towel you may have a nasty surprise lurking in wait.
Remember that the windows are plastic and whenever possible, prior to putting any rag or towel on them, you should flush the surface with water. I know that's not always possible but even carrying a water bottle helps to lengthen the life of your windows.