Dynamic graphs are widely used to represent evolving real-world networks. Temporal Graph Neural Networks (TGNNs) have emerged as a powerful tool for processing such graphs, but the lack of transparency and explainability limits their practical adoption. Research on TGNN explainability is still in its early stages and faces several key issues: (i) Current methods are tailored to specific TGNN types, restricting generality. (ii) They suffer from high computational costs, making them unsuitable for large-scale networks. (iii) They often overlook the structural connectivity of explanations and require prior knowledge, reducing user-friendliness. To address these issues, we propose GRExplainer, the first universal, efficient, and user-friendly explanation method for TGNNs. GRExplainer extracts node sequences as a unified feature representation, making it independent of specific input formats and thus applicable to both snapshot-based and event-based TGNNs (the major types of TGNNs). By utilizing breadth-first search and temporal information to construct input node sequences, GRExplainer reduces redundant computation and improves efficiency. To enhance user-friendliness, we design a generative model based on Recurrent Neural Networks (RNNs), enabling automated and continuous explanation generation. Experiments on six real-world datasets with three target TGNNs show that GRExplainer outperforms existing baseline methods in generality, efficiency, and user-friendliness.