In the DC comics, Detonator is a master assasin and explosives expert who was part of the Seven Men of Death, a faction of the League of Assassins.
Kate spends most of the episode (and an in-universe week) refusing to don the cowl again, due to feeling like she doesn't deserve it.
The episode had elements similar to the horror movie franchise "Saw" where people awoke and had to play a tape to hear that either they were gonna die or someone else was. Coincidentally, Jigsaw (2017), aka "Saw 8" premiered on the Syfy Channel at the same time the episode was airing.
The speech Luke gives to Kate that mentions an abyss is likely a reference to the famous Friedrich Nietzsche quote, which says to "beware that, when fighting monsters, you yourself do not become a monster...for when you gaze long into the abyss. The abyss gazes also into you."
Luke points out the irony in Kate connecting the 214 the original Detonator left behind to the discharge code DD-214, the same one that was put on her own discharge forms from the military academy. Essentially, getting discharged from the academy helped her solve a case even Bruce couldn't solve.