Owing to the importance of training datasets in the performance of AI systems, recent work in XAI has focused on communicating information about training datasets to stakeholders. While explaining this information can bring many potential benefits for the receivers, like other AI explanations, they can also bring negative consequences. In this position paper, we describe how we can use training dataset explanations to study the negative consequences of explanations and to explore potential mitigation strategies. We discuss potential challenges that researchers might face in these explorations.