It's most likely buildup on the inside of the windshield. Get a mixture of 50/50 water and isopropyl alcohol 70% for your cleaning solution and a waffle weave MF towel. You might have to do multiple passes to get it clean. Do it for the inside and outside of the windshield, and following
tips to save when replace broken windshield can help, always using a clean side of the towel for final wipe.
I'm on windshield #2 from Safelite, no issues with the second one. Just had it replaced a couple of months ago for a crack in the corner.