Accurately classifying the relevance of Query-Product pairs is critical in online retail stores such as Amazon, as displaying irrelevant products can harm user experience and reduce engagement. While Large Language Models (LLMs) excel at this task due to their broad knowledge and strong reasoning abilities. However, their high computational demands constrain their practical deployment in real-world applications. In this paper, we propose a novel distillation approach for e-commerce relevance classification that uses “rationales” generated by LLMs to guide smaller cross-encoder models. These rationales capture key decision-making insights from LLMs, enhancing training efficiency and enabling the distillation to smaller cross-encoder models deployable in production without requiring the LLM. Our method achieves average ROC-AUC improvements of 1.4% on 9 multilingual e-commerce datasets, 2.4% on 3 ESCI datasets, and 6% on GLUE datasets over vanilla cross-encoders. Our 110M parameter BERT model matches 7B parameter LLMs in performance (< 1% ROC-AUC difference) while being 50 times faster per sample.