Hey Jaybird - that stuff is actually important for how the vapor is made. That is the internal wicking that sits above the atomizer wire. They are there to move liquid from the steel mesh "bridge" to above the coil to be vaporized. There are more 'strings' than that under the bridge.
The burning is usually caused by not having enough liquid in your atomizer/cart or by chain
vaping and causing the temps to raise inside the atty (pilot error).
Some people think doing a dry burn is cleaning the atomizer, when in fact, it is usually burning these wicking
threads and causing problems later.
I just boiled out a 510 that had a nasty taste this morning (in the microwave for about 2 minutes) which is a last resort for me. A small dark brown piece came out on its own, and now the burned taste is gone. I suspect it was loose and hanging down in the pot or something. Probably a manufacturing mishap. If you spot one sticking out and it is pretty dark (and you are experiencing a bad burned taste), you can try to remove it, but you take the risk of ruining your atomizer.
Many who have removed the threads report that the atty doesn't work right anymore. Some say they've removed them with no problem, but I suspect there is still some left under the bridge that they aren't seeing.
This is an interesting thread
http://www.e-cigarette-forum.com/fo...ent/18148-some-coil-wicks-really-do-burn.html
and (old thread but it shows some of the early findings for those threads)
http://www.e-cigarette-forum.com/fo...ufacturers-suppliers-whats-my-atomizer-3.html