Mortgage rates in the next 2 weeks…

I am currently in escrow on a house and the closing date is June 16. Two weeks ago we locked in our mortgage rate at 6.375. However, we get a second bite at the apple with our lender. Basically, we can ask our lender to rerun the rate, and if it has dropped below a certain threshold, our rate will reduce by a degree. However, we only get to ask once. So my question: based on where the rates are since the debt felling fiasco has resolved, any advice on when the best time is to ask for a reduced rate? We have until 6/15 to see if we can get it down. I don’t want to ask too soon and not benefit. But I also don’t want to wait too long and end up with the same rate if I can help it.