Online peer counseling platforms enable conversations between millions of people seeking and offering mental health support. Among counseling skills, reflective listening, i.e., capturing and returning to the client something the client has said, is important for positive therapeutic outcomes. We introduce a reflection generation system for online mental health support conversations leveraging GPT-3, a large language model. We compare few-shot learning against fine-tuning and assess the impact of the quality of training examples as measured by fluency, reflection resemblance, and overall preference. Fine-tuned GPT-3 generates responses that human evaluators rate as comparable in reflection quality to responses used for tuning. Models based on high-quality responses generate substantially better reflections than ones tuned on actual responses from a large online counseling service–and better reflections than the actual counselor responses. These results suggest the care needed in selecting examples for tuning generative models.