Just catch the shreds as best you can, and stick them back together. This stage means you're halfway done. You be completely done when the gluten is a rubbery ball and the water dripping off of it is clear instead of coudy. Asian cultures tend to waste nothing, so when the rinse water becomes thick and white with starch, it's poured into another container, and left for the starch to settle to the bottom. The clear upper water is poured off, and the starch is kept for thickening in cooking.
Some sources say to alternate warm and cold rinses.
One says to go from warm to cold. Some don't mention rinsing temperature at all. Using this method, you can mix dry seasonings like herbs and chili powder in with the gluten flour, and you can mix wet flavorings like shoyu, miso, oil, and blended vegetables with the wet ingredients. Some people put garlic or onion powder in with the gluten flour, but I find them to have such an lingering and rancid aftertaste that I regret even tasting any food that contains them. Any leftover slurry goes into the simmering broth.