The problem of data exchange involves a source schema, a target schema and a set of mappings from transforming the data between the two schemas. We study the problem of data exchange in the presence of privacy restrictions on the source. 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. We propose a protocol that provides formal privacy guarantees and is data-independent, i.e., if certain criteria are met, then the protocol guarantees that the mappings leak no sensitive information independently of the data that lies in the source. We also propose an algorithm for repairing an input mapping w.r.t. a set of policy views, in cases where the input mapping leaks sensitive information. The empirical evaluation of our work shows that the proposed algorithm is quite efficient, repairing sets of 300 s-t tgds in an average time of 5s on a commodity machine. To the best of our knowledge, our work is the first one that studies the problems of exchanging data and repairing mappings under such privacy restrictions. Furthermore, our work is the first to provide practical algorithms for a logical privacy-preservation paradigm, described as an open research challenge in previous work on this area.