Maybe they think that it will make it more interesting. I think it identifies them and makes them more significant and sort of distinguishes them. Like this tatoo shows that you are part of the pack. That kind of thing.
The tattoos are to symbolize that they are part of the pack. It's not metioned in the book, but books are different than movies. Books get into the mind of the character, but movies are visual; you need a physical way to represent the pack. That's why the movie producers made the tattoo.