Remote Patient Management systems (RPM) are crucial for addressing healthcare workforce shortages. These systems are often designed with a specified focus on clinical functionalities, without proper consideration for human-centric concerns. A care perspective is essential not only to acknowledge patients as people, but also to foster better quality of care and, ultimately, adoption. This highlights the gap of how RPM can embed caring. This work offers a systematic literature review aimed at developing "Caring RPM", a normative framework that integrates the philosophy of caring from nursing theory into RPMs. This framework underwrites the practical, moral, and relational aspects of patient care, including actionable recommendations to recalibrate RPM systems for more effective human-centric design. The framework can inspire new ways of embedding the caring dimension into HCI design practices.