Veganism is about doing everything possible to avoid the use of animals and their products. This is the definition of vegan according to the Vegan Society:
"A philosophy and way of living which seeks to exclude—as far as is possible and practicable—all forms of exploitation of, and cruelty to, animals for food, clothing or any other purpose; and by extension, promotes the development and use of animal-free alternatives for the benefit of humans, animals and the environment. In dietary terms it denotes the practice of dispensing with all products derived wholly or partly from animals."
We killed nits, and kill other parasites. deterring them as far as possible is always preferable from any point of view. I avoid killing intruding wasps and other one off visitors, rescue worms from pavements, but self preservation allows for killing parasites and taking medicines.
Rather than suggesting posters google: www.vegansociety.com/go-vegan/definition-veganism