Tattooes usually are ink on skin. For mobians tattoos work as permanently dyeing fur or shaving/surgically removing their fur in order to get one. Tattoos most commonly for mobians are done on the face and tattoos are normalized in nowadays's mobian culture, just like fur or skin markings that come naturally. It blends with the rest and most respect mobians who get tattoos.
Mobians with scales tend to scratch/dent their scales and then color them in with ink. Some take it as far as injuring themselves, dyeing their scar and leaving it forever that way. Of course, that often can go wrong and some die from it.
There have been efforts to decrease it, by trying to use alternative methods of just sticking some fake-skin on top of a scale, that is layered under their pattern, though that option only applies to simple patterns.
PSA's about body-art for lizards have been made, so they stop injuring themselves in the process for freedom of self-expression.