We investigate the rate distortion tradeoff in private read update write (PRUW) in relation to federated submodel learning (FSL). In FSL a machine learning (ML) model is divided into multiple submodels based on different types of data used for training. Each user only downloads and updates the submodel relevant to its local data. The process of downloading and updating the required submodel while guaranteeing privacy of the submodel index and the values of updates is known as PRUW. In this work, we study how the communication cost of PRUW can be reduced when a pre-determined amount of distortion is allowed in the reading (download) and writing (upload) phases. We characterize the rate distortion tradeoff in PRUW along with a scheme that achieves the lowest communication cost while working under a given distortion budget.