Editors of academic journals and program chairs of conferences require peer reviewers to write their own reviews. However, there is growing concern about the rise of lazy reviewing practices, where reviewers use large language models (LLMs) to generate reviews instead of writing them independently. Existing tools for detecting LLM-generated content are not designed to differentiate between fully LLM-generated reviews and those merely polished by an LLM. In this work, we employ a straightforward approach to identify LLM-generated reviews - doing an indirect prompt injection via the paper PDF to ask the LLM to embed a watermark. Our focus is on presenting watermarking schemes and statistical tests that maintain a bounded family-wise error rate, when a venue evaluates multiple reviews, with a higher power as compared to standard methods like Bonferroni correction. These guarantees hold without relying on any assumptions about human-written reviews. We also consider various methods for prompt injection including font embedding and jailbreaking. We evaluate the effectiveness and various tradeoffs of these methods, including different reviewer defenses. We find a high success rate in the embedding of our watermarks in LLM-generated reviews across models. We also find that our approach is resilient to common reviewer defenses, and that the bounds on error rates in our statistical tests hold in practice while having the power to flag LLM-generated reviews, while Bonferroni correction is infeasible.