I dunno ...
For one Kithrak (as far as i know, one of higher ranks) is certainly someone who will know their society much better than a youngling, who didnt even finished her mature ritual.
For two, if you create a Githyanki, you dont even know about the Purification (or at least last time i tryed, my Gith had only one option and that was "i never heared about this") ... also i wonder if our PC Gith is also concidered child or allready Mature ... that would be funny as hells, concidering how Lae'zel is talking to us, who would be in fact allready superior for her.
But, it might be that Kithrak simply decided to go the path of less resistance ... and kill her right now, than spend resources (mostly time) for her healing. :-/
After all, if there is something that all "low rank soldiers" have in common, its the fact that they are often seen as expendable by their superiors.