Tea is made from plants. All plants have proteins. The parts of the plant that we eat may or may not be a good source of protein for humans.
Practically all Chinese, Indian, and English teas are all made from the same species of plant, Camellia sinensis, simply known as a tea tree. If you were to eat the leaves they would be a good source of protein and fiber, not to mention vitamins and antioxidants. However, we discard the leaves with the fiber, and typical ways of preparing the leaves and the tea can decrease the protein and antioxidants. Its possible your brand flash freezes tthe leaves or uses some other method to try and preserve these nutrients. Ive seen some English teas that are powder you mix in instead of steeping, and this would work as well. In fact, tea leaves are absolutely edible! If you get a decent to high quality tea you can take your leaves after you make tea and throw them in a smoothie, soup, or even eggs and youll get the rest of the nutrients left in them and wont be thowing food in the bin.
Most food contains bugs. Its unlikely that it would be a large enough quantity to change the nutrition labels.