Generative adversarial networks (GANs) have emerged as powerful tools for generating realistic images in various domains, including healthcare and medicine. However, concerns surrounding the privacy and security of personal data have become prominent. This study investigates the presence of fingerprints in synthetic medical images generated by GANs, which may indicate traces of the real images used during training and raise concerns about the sharing and limitations imposed by sensitive medical data. To address this, we analyze the texture characteristics of real and synthetic images from the ImageCLEF2023 Medical GANs challenge datasets, utilizing a range of texture descriptors and analysis methods to identify discernible patterns within the synthetic image data and determine the source images employed for training. We calculate the cumulative distribution function (CDF) of texture feature maps and apply the Wasserstein distance to compare the CDFs of the query and generated images. A binary classifier is trained to predict the utilization of the query image in generating each GAN image. The obtained results demonstrate balanced performance across various evaluation metrics, with the model exhibiting good generalization to the challenge test set, achieving an accuracy of 0.54 and an F1-score above 0.5. Our findings provide valuable insights into the security and privacy considerations when generating and utilizing artificial medical images in real-life scenarios.