We study the interactive compression of an arbitrary function of two discrete sources with zero-error. The information on the joint distribution of the sources available at the two sides is asymmetric, in that one user knows the true distribution, whereas the other user observes a different distribution. This paper considers the minimum worst-case zero-error codeword length under such asymmetric prior distributions. We investigate the cases for which reconciling the information mismatch is better or worse than not reconciling it, but instead using an encoding scheme that ensures zero-error with possibly increased communication rate. Our results indicate a reconciliation-communication tradeoff and that there exist cases for which partially reconciling the mismatched information is better than both perfect reconciliation and no reconciliation.