How to recover cast iron skillet with melted fiber on it
First, you should never scrub cast iron with a brillo pad, as the steel in the brillo is harder than the cast iron, and can not only strip off the seasoning but scratch up the iron itself.  The same would be true with sandpaper or a dremel.

Instead, you should plan to completely strip and reseason the pan, using lye or oven cleaner (scroll down a couple pages in that article).

If it is only the handle that is a mess, use the oven cleaner method to just strip the handle (protecting the rest of the pan with a plastic bag), then continue the seasoning process.  The handle will end up with fewer layers of seasoning than the rest of the pan, but that's fine, it's just the handle and not a cooking surface.

Alternately, if you can heat the pan in a well-ventilated area (an outdoor grill, for example), you may be able to simply burn off the fibers, depending on what they are made of (if they have a silicone or metallic coating, probably not).  In this case, just heating the pan to more than 500F/250C for a couple hours may take care of the problem, and can even be part of the seasoning process.

Finally, if you plan to handle the hot pan during seasoning again, get some welding gloves.