Generative models, particularly text-to-image (T2I) diffusion models, play a crucial role in medical image analysis. However, these models are prone to training data memorization, posing significant risks to patient privacy. Synthetic chest X-ray generation is one of the most common applications in medical image analysis with the MIMIC-CXR dataset serving as the primary data repository for this task. This study presents the first systematic attempt to identify prompts and text tokens in MIMIC-CXR that contribute the most to training data memorization. Our analysis reveals two unexpected findings: (1) prompts containing traces of de-identification procedures (markers introduced to hide Protected Health Information) are the most memorized, and (2) among all tokens, de-identification markers contribute the most towards memorization. This highlights a broader issue with the standard anonymization practices and T2I synthesis with MIMIC-CXR. To exacerbate, existing inference-time memorization mitigation strategies are ineffective and fail to sufficiently reduce the model's reliance on memorized text tokens. On this front, we propose actionable strategies for different stakeholders to enhance privacy and improve the reliability of generative models in medical imaging. Finally, our results provide a foundation for future work on developing and benchmarking memorization mitigation techniques for synthetic chest X-ray generation using the MIMIC-CXR dataset. The anonymized code is available at https://anonymous.4open.science/r/diffusion_memorization-8011/