The answer to this will depend on your zucchini and your gut instincts. Some people do and some people don't. If you are using large garden zucchini, not only might you want to peel it because the skin is thicker and more bitter, but you may also want to squeeze it out as it may contain more water than grocery store zucchini. If you're using your regular market zucchini you don't have to squeeze the water out. However, if you notice it is very watery, you can do it anyway. Either way, it doesn't hurt to pat the grated zucchini with a paper towel.