Jane
When I read your post about the "dots" for quilting, it reminded me of some embroidery that I had done, using DMC, for a quilt top. On my FIRST one, I got part of it wet somehow, probably from my water bottle, and ended up with what looked like a splotch of blue thread that "ran" and paniced immediately -- but it was just the dye in the embroidery panel when it was wet. Since it's supposed to come off, it doesn't take much for it to come off, even sweaty hands can do it. Once I washed it, it was perfectly fine, as all the residue of the pre-marking came off. Since the area where your thread is located would be on top of a pre-marked line, are you certain that it is from the thread and not from the marking underneath the thread? If this is a possible cause, I'd go ahead and quilt it, wash it with a color-catcher, and it might be just perfect. If not, then you could try the suggested remedies.