If the nests are small enough and the threads are really close together, you could pull them out from the back of the quilt until you have a long enough piece of the top and bottom thread and tie them together in a small, tight knot. Or, just pull out as few stitches as possible, clip, and resew.
Nests can be caused when you change directions while FMQ and you are not moving the fabric as fast, or as slow, as your machine speed. That same thing will also cause loops on the back of your quilt. If your machine speed is slow, your FMQ should also be slow. As you practice, you'll know if you do better at a slow, medium, or fast speed.