Confidential computing (CC) or trusted execution enclaves (TEEs) is now the most common approach to enable secure computing in the cloud. The recent introduction of GPU TEEs by NVIDIA enables machine learning (ML) models to be trained without leaking model weights or data to the cloud provider. However, the potential performance implications of using GPU TEEs for ML training are not well characterized. In this work, we present an in-depth characterization study on performance overhead associated with running distributed data parallel (DDP) ML training with GPU Trusted Execution Environments (TEE). Our study reveals the performance challenges in DDP training within GPU TEEs. DDP uses ring-all-reduce, a well-known approach, to aggregate gradients from multiple devices. Ring all-reduce consists of multiple scatter-reduce and all-gather operations. In GPU TEEs only the GPU package (GPU and HBM memory) is trusted. Hence, any data communicated outside the GPU packages must be encrypted and authenticated for confidentiality and integrity verification. Hence, each phase of the ring-all-reduce requires encryption and message authentication code (MAC) generation from the sender, and decryption and MAC authentication on the receiver. As the number of GPUs participating in DDP increases, the overhead of secure inter-GPU communication during ring-all-reduce grows proportionally. Additionally, larger models lead to more asynchronous all-reduce operations, exacerbating the communication cost. Our results show that with four GPU TEEs, depending on the model that is being trained, the runtime per training iteration increases by an average of 8x and up to a maximum of 41.6x compared to DDP training without TEE.