We address the detection of emission reduction goals in corporate reports, an important task for monitoring companies' progress in addressing climate change. Specifically, we focus on the issue of integrating expert feedback in the form of labeled example passages into LLM-based pipelines, and compare the two strategies of (1) a dynamic selection of few-shot examples and (2) the automatic optimization of the prompt by the LLM itself. Our findings on a public dataset of 769 climate-related passages from real-world business reports indicate that automatic prompt optimization is the superior approach, while combining both methods provides only limited benefit. Qualitative results indicate that optimized prompts do indeed capture many intricacies of the targeted emission goal extraction task.