Exchanging data between data sources is a fundamental problem in many data science and data integration tasks. In this paper, we focus on the data exchange problem in the presence of privacy constraints on the source data, which has been disregarded in the literature to date. By leveraging a logical privacy-preservation paradigm, the privacy restrictions are expressed as a set of policy views representing the information that is safe to expose over all instances of the source in order to exchange them with the target. We introduce a protocol that provides formal privacy guarantees and is data-independent, i.e., under certain criteria, it guarantees that the mappings leak no sensitive information independently of the instances lying in the source. Moreover, we design an algorithm for repairing an input mapping w.r.t. a set of policy views, in cases where the input mapping leaks sensitive information. We show that the repairing can build upon hard-coded and learning-based user preference functions and we show the trade-offs. Our empirical evaluation shows that repairing mappings is quite efficient, leading to repairing sets of 300 s-t tgds in an average time of 5s on a commodity machine. It also shows that the repairing based on learning is robust and has comparable runtimes with the hard-coded one.