Thank you all for your replies. As I said initially, they are a very reputable shop and had redone 2 windows for me in the past for similar imperfections. The main difference here is that a windshield is huge and statistically more likely to have imperfections.
In the end I couldn't live with it. I had them redo it, which they did without much fuss, and it is now perfect. They are a little more expensive than surrounding shops but clearly worth every penny. The older I get, the more I am happy to pay for good work.