We provide a summary of discussions at the week-long tele-workshop “Pion and Kaon Structure Functions at the EIC”, held in June 2020 under the auspices of the Center for Frontiers in Nuclear Science. The presentations and attendant conversations provided a perspective on existing challenges and future opportunities as experiment, phenomenology, and theory reach toward the goals of revealing the origin and consequences of emergent hadronic mass using modern and planned facilities. The potential for discovery at modern and planned facilities was highlighted, with emphasis on the electron ion collider.