Capturing organization-specific domain knowledge remains a critical challenge for deploying cost-efficient language models in specialized tasks like contact center Quality Assurance (QA). While large LMs implicitly capture expert judgment, smaller LMs require explicit evaluation criteria that domain experts struggle to articulate. We introduce Backward Question-based Refinement (BQR), a diagnostic framework that generates backward questions, revealing what a model understood rather than what was asked, to systematically distill implicit reasoning from large LMs into explicit evaluation plans. Through experiments on 12 QA questions, BQR achieves performance improvements on 8 questions with absolute gains of up to 27.8% in Macro F1. Our analysis establishes empirical parallels to gradient-descent optimization and reveals a cross-family advantage where small LMs benefit more from large LMs of different families. These findings confirm BQR as an effective approach for bridging the gap between implicit expert knowledge and explicit evaluation criteria.