Can I identify window manufacture from the NAMI information?
I would recommend you just make the Window screen yourself.  They are really easy to make and I am sure you can find a clip option that will fit your needs.  Besides, if these are contractor windows, you probably can't get the OEM screen anymore and/or the manufacturer no longer exists.

Here is an example screen parts supplier: http://www.qualitywindowscreen.com/screening-supplies-parts-tools.html

Here is an example video showing how easy the screens are to build:
https://www.youtube.com/watch?v=MxZHslZduRw