|I've had the dubious 'pleasure' of doing this twice recently, and have been salvaging the original thread as I go, because there was not a good replacement thread match.
I was worried about breaking the threads as I eased them out with the stem of my quick unpick tool. So I started using a thin wooden satay/shaslik skewer ( about 6 inches/15cms long) which I use for easing fabric under the machine needle. I have sharpened the stick so that the point has a TINY flat bit -like a chisel- that I then push under the topstitched stitch, before lifting the stitch and pushing the stem of the stick under the lifted stitch. Then I roll the stick with my fingers, easing the stitch out at the same time. As the stick is smooth and round, I have had no worries about breaking the thread when using this method. It is just as fast as using the unpicking tool, maybe even faster, once you get the rhythm.