In calculations of the transferred hyperfine field at ligand-ion nuclei in transition-metal compounds, overlap and covalency effects are usually accounted for, but the exchange-core polarization of ligand closed electron shells due to the unpaired metal-ion orbitals are neglected. We have calculated this interaction for ZnF2: Mn, using the moment-perturbation technique and a model of free-ion orbitals distorted only by overlap. We find that the net contribution in this case is small because of an interesting cancellation of large individual terms. The hyperfine field at the Mn55 nucleus arises from exchange polarization of the s cores by the unpaired Mn++ d orbitals. In the crystal, both the core s and valence d orbitals are distorted by overlap, and thus the hyperfine field at the Mn++ nucleus is changed from the free-ion value. The major overlap contribution is found to arise from the Pauli distortion of the Mn++ s-core orbitals by surrounding ligand orbitals, and this effect is shown to decrease the magnitude of the free-ion value, in agreement with experiment.