Last night, I was thinking about an AU where Inej gets tattoos some time in the future because she chooses to reclaim them after the Menagerie made them something awful for her. That marking herself, as her choice, could be a good thing she finds.
Also the idea that eventually Inej decides she does want a Dregs tattoo to mark the influence of them on her life there, to not be ashamed of her past or the choices she made to survive. But only if Kaz gives the tattoo to her. Except, Kaz is not a tattoo artist and cannot bear the idea of creating a bad tattoo aesthetically, let alone on Inej of all people.
He's not sure if it's meant to be an impossible to fulfil request from Inej, but of course he intends to quietly make it possible in case she actually means it. He's perfectionist about practicing while she's away; first on fruit, then on himself with small designs - carefully planned so if they go wrong they can at least be covered up with something better later on. Once he's confident enough for others to see his work, he practices more by giving the new Dregs recruits their tattoos until he gets good enough he's satisfied it's time.
And when he does do the tattoo on her request once Inej returns, he modifies the design so it includes knives and saints imagery so that the Dregs is not him owning her with the mark, but both of them ruling the gang together with people who only ever choose to take their mark.