Deep neural networks often suffer performance degradation upon deployment due to distribution shifts. Continual Test-Time Adaptation (CTTA) aims to address this issue in an unsupervised manner, yet existing methods, which rely on self-supervision, are prone to an inherent self-referential feedback loop that amplifies initial prediction errors, leading to model drift. We revisit this limitation and propose Test-Time Distillation (TTD), which reframes adaptation as a distillation process guided by a frozen Vision-Language Model (VLM) as an external signal. While promising, we find that direct distillation is fraught with two pitfalls: the Generalist Trap, where the VLM's broad but non-specialized knowledge leads to suboptimal performance on specific tasks and shifts, and the Entropy Bias, where naive model fusion techniques based on entropy fail due to the disparate calibration of heterogeneous models. These pitfalls motivate our insight: the key is to build a robust supervisory signal and leverage it to guide the target model toward stable adaptation. Hence, we present CoDiRe, a Continual Distillation and Rectification framework for TTD. CoDiRe first constructs a robust blended teacher by dynamically fusing the predictions of the VLM and the target model. Critically, it circumvents the Entropy Bias by leveraging Maximum Softmax Probability (MSP) as a more reliable confidence metric for weighting each model's expertise. Then applies an Optimal Transport based rectification to further align predictions with the blended teacher, enabling continuous and stable adaptation. Extensive experiments show that CoDiRe outperforms state-of-the-art baselines, exceeding CoTTA by 10.55% while using only 48% of its time cost on ImageNet-C.