Health misinformation spreading online poses a significant threat to public health. Researchers have explored methods for automatically generating counterspeech to health misinformation as a mitigation strategy. Existing approaches often produce uniform responses, ignoring that the health literacy level of the audience could affect the accessibility and effectiveness of counterspeech. We propose a Controlled-Literacy framework using retrieval-augmented generation (RAG) with reinforcement learning (RL) to generate tailored counterspeech adapted to different health literacy levels. In particular, we retrieve knowledge aligned with specific health literacy levels, enabling accessible and factual information to support generation. We design a reward function incorporating subjective user preferences and objective readability-based rewards to optimize counterspeech to the target health literacy level. Experiment results show that Controlled-Literacy outperforms baselines by generating more accessible and user-preferred counterspeech. This research contributes to more equitable and impactful public health communication by improving the accessibility and comprehension of counterspeech to health misinformation.