The prior owner got the windshield replaced by a company that clearly sucks. They just ran a fat bead of schmoo across the top and stuck in some generic seal that ended up blowing off one day on the freeway. I ordered a new finisher strip but not too sure how to properly install it. I think it just friction fits into the windshield, but the caulking the windshield installer used is clearly interfering with that. Oh, and it leaks. So there's that too.

 

Curious as well. I had my windshield replaced by a mobile Safelite clown some time ago. Looks like he re-used the OEM seal - lumpy as hell...

 

i had mine done by a safelite mobile unit a couple of years ago. i stuck around and watched what he was doing because there were clearly some parts of the process that required special attention. i have the heated windshield but i don't think that makes any difference at the top of the glass.
what i do recall is that there was some special piece along one edge that had to be fitted to the glass prior to the installation, and that it took the two of us and some mallet-related coaxing to get it into place. the safelite instructions were clear but it was a fiddly job to get it right. they also stated that the windshield WOULD leak if the piece was not fitted correctly. unfortunately, i don't remember if it was at the top of the windshield or at the bottom.

rather than trying to patch up a bad job, could you try contacting your insurance company to see about your glass coverage? a full removal and reinstall might be the best approach. of course, your a-pillars and cowl WILL break as part of that process.