Kirk: Let me in there. I can help her. Hodin: We have no need of any of your medicines.
Kirk: But she's ill!
Hodin: And we are grateful to you for her illness. You have done well, my daughter. Guard the captain well. We shall need him for a long time.
Kirk is finding out that there was no transporter accident and that it was all a setup by the people of Gideon. They wanted him to pass on sickness and disease to their people to help their overpopulation problem.