Heterogeneous ice nucleation at solid surfaces impacts many areas of science, from environmental processes, such as precipitation, to microbiological systems and food processing, but the microscopic mechanisms underpinning nucleation remain unclear. Discussion of ice growth has often focused around the role of the surface in templating the structure of water, forcing the first layer to adopt the registry of the underlying substrate rather than that of ice. To grow a thick ice film, water in the first few ice layers must accommodate this strain, but understanding how this occurs requires detailed molecular-scale information that is lacking. Here we combine scanning tunneling microscopy, low-energy electron diffraction, and work-function measurements with electronic structure calculations to investigate the initial stages of ice growth on a Pt alloy surface, having a lattice spacing 6% larger than ice. Although the first layer of water forms a strictly commensurate hexagonal network, this behavior does not extend to the second layer. Instead, water forms a 2D structure containing extended defect rows made from face-sharing pentamer and octamer rings. The defect rows allow the majority of second-layer water to remain commensurate with the solid surface while compensating lateral strain by increasing the water density close to that of an ice surface. The observation of octamer-pentamer rows in ice films formed on several surfaces suggests that the octamer-pentamer defect motif acts as a flexible strain relief mechanism in thin ice films, providing a mechanism that is not available during the growth of strained films in other materials, such as semiconductors.