In the DC Comics, Mary Elizabeth "Bette" Kane is the original Bat-Girl and served as Batwoman's sidekick and Robin's counterpart. Growing up she would adopt the alias Flamebird (and later Hawkfire) in response to her counterpart's development as Nightwing. In the comics she is Kate Kane's younger cousin instead of her step-sister.
Batwoman clearly has black paint around her eyes whenever she wears the cowl. But whenever she takes the cowl off, there's never any paint around her eyes. This happens in several episodes and is common amongst many superhero/comic book shows with masked characters.
