Impact cratering creates a wide range of topography on small satellites and asteroids. The population of visible craters evolves with impacts, and because there are no competing endogenic processes to modify the surface, determining the various ways younger craters add to or subtract from the population is a fundamental aspect of small-body geology. Asteroid 433 Eros, the most closely studied small body, has regions of substantially different crater densities that remain unexplained. Here we show that the formation of a relatively young crater (7.6 km in diameter) resulted in the removal of other craters as large as 0.5 km over nearly 40 percent of the asteroid. Burial by ejecta cannot explain the observed pattern of crater removal. The limitation of reduced crater density to a zone within a particular straight-line distance through the asteroid from the centre of the large crater suggests degradation of the topography by seismic energy released during the impact. Our observations indicate that the interior of Eros is sufficiently cohesive to transmit seismic energy over many kilometres, and the outer several tens of metres of the asteroid must be composed of relatively non-cohesive material.