The chemical effects of terrestrial alteration, with a particular focus on lithophile trace elements, were studied for a set of H chondrites displaying various degrees of weathering from fresh falls to altered finds collected from hot deserts. According to their trace element distributions, a considerable fraction of rare earth elements (REEs), Th, and U resides within cracks observed in weathered meteorite specimens. These cracks appear to accumulate unbound REEs locally accompanied by Th and U relative to the major element abundances, especially P and Si. The deposition of Ce is observed in cracks in the case of most of the weathered samples. Trace element maps visually confirm the accumulation of these elements in such cracks, as previously inferred based on chemical leaching experiments. Because the positive Ce anomalies and unbound REE depositions in cracks occur in all weathered samples studied here while none of such features are observed in less altered samples including falls (except for altered fall sample Nuevo Mercurio), these features are interpreted to have been caused by terrestrial weathering following chemical leaching. However, the overall effects on the bulk chemical composition remain limited as the data for all Antarctic meteorites studied in this work (except for heavily weathered sample A 09516, H6) are in good agreement with published data for unaltered meteorites.