So like.. when Korra becomes an air bender she'll get the tattoos? I'm only half way through the show so... sweatdrop
... they're tattoos that Air Nomads get once they've fully mastered airbending. since Korra isn't an Air Nomad there's no indication she'd ever get them. and if you paid attention you'd see there's no proof any past Avatars that weren't Air Nomads ever got those tattoos.