The structure of a two-dimensional vortex liquid in the presence of strong pinning centers is investigated using the density-functional formalism. Short-range positional and angular correlations in the liquid result in an effective interaction between pinned vortices, mediated by the unpinned ones. This effective interaction is short range and it oscillates with the intervortex distance. Matching of this oscillation with a periodic array of strong pinning centers leads to anomalies in the reversible magnetization M(H) at the ``matching field″ B-phi and some of its harmonics.