Scientific peer review generation has attracted increasing attention for reducing reviewing burdens and providing timely feedback. However, existing Large Language Model (LLM)-based methods often produce generic comments with insufficient evidence support and weak source traceability, while complex multi-agent systems incur high inference costs. To address these challenges, we propose EGTR-Review, an Evidence-Grounded and Traceable Review Generation framework via Multi-Agent Teacher Distillation. EGTR-Review first constructs a multi-agent teacher that performs structure-aware paper decomposition, key-element extraction, external scholarly evidence retrieval, evidence-state labeling, verification reasoning, and review synthesis. It then distills both intermediate reasoning trajectories and final review comments into a lightweight student model through task-prefix-driven multi-task learning. An evidence-weighted objective further reduces the influence of weak, missing, or non-verifiable supervision. Experiments on public peer-review datasets show that EGTR-Review (Student) outperforms strong prompt-based, fine-tuned, and structured/agentic baselines across automatic metrics, LLM-as-Judge evaluation, and human evaluation, while maintaining strong factual grounding and source traceability with substantially lower token consumption and inference time. Our code, prompts, configurations, and sample data are available on GitHub.