The widespread availability of cell phones has enabled non-profits to deliver critical health information to their beneficiaries in a timely manner. This paper describes our work to assist non-profits that employ automated messaging programs to deliver timely preventive care information to beneficiaries (new and expecting mothers) during pregnancy and after delivery. Unfortunately, a key challenge in such information delivery programs is that a significant fraction of beneficiaries drop out of the program. Yet, non-profits often have limited health-worker resources (time) to place crucial service calls for live interaction with beneficiaries to prevent such engagement drops. To assist non-profits in optimizing this limited resource, we developed a Restless Multi-Armed Bandits (RMABs) system. One key technical contribution in this system is a novel clustering method of offline historical data to infer unknown RMAB parameters. Our second major contribution is evaluation of our RMAB system in collaboration with an NGO, via a real-world service quality improvement study. The study compared strategies for optimizing service calls to 23003 participants over a period of 7 weeks to reduce engagement drops. We show that the RMAB group provides statistically significant improvement over other comparison groups, reducing ~30% engagement drops. To the best of our knowledge, this is the first study demonstrating the utility of RMABs in real world public health settings. We are transitioning our RMAB system to the NGO for real-world use.