Derek is tasked with taking care of Minco, and being responsible for her in the after life.

He was the one to kill her in the story, however after she mellowed out and her disease began to fade away, he began showing her more compassion and care.
Neither of them have an issue with being nude in front of each other, as they both come from places that don't see it as sexual or taboo. It's just the best way to check for wounds after a nasty fight, which is what's happening here! She's got a hand injury, but aside from that she seems alright.