I brewed up a pot just so I could get a look first hand. I guess I never tried pulling the nuggets apart. The strings are smaller than I imagined after reading your post.
I know nothing about chemistry, but I wonder if these little strings are actually proteins that have been developed in the tea "sludge" that the nuggets are made of. Through friction or pressure, together with drying and aging, I could imagine something like that developing in the juices that cling to machine parts, much like flour develops elastic gluten in response to kneading. I think a stringy texture in organic things, like mozzarella, usually indicates proteins. My tendency is to think that the strings are a natural development in this material and there is nothing added to make it stick together.