This paper explores the design space of feedback systems that connect care recipients to the community health feedback loop. While related work in this vein has often emphasized gathering feedback for the sake of transparency alone, our study emphasizes opportunities to integrate the collection and use of feedback in ways that may improve the quality or equity of routine health services. We conducted a qualitative study using semi-structured interviews and focus groups with 23 participants in Kenya. Our field study makes current feedback practices visible; and reveals barriers faced by beneficiaries, community health workers, and their supervisors. Our findings identify relevant socio-technical complexities, and we outline concrete opportunities to design feedback systems that support and augment current practices. These contributions to the ICTD literature hold potential to inform the design of feedback systems that engage underserved populations in a systematic and equitable manner.