The observed O 1s X-ray photoemission spectra of the cuprate superconductors often exhibit a satellite at a higher binding energy to the main peak. The origin of this satellite is not fully understood. We have done model cluster calculations to investigate the origin of this satellite using the configuration interaction approach. The calculated spectra for the divalent and superconducting cuprates essentially exhibit a single peak. On distorting the cluster in-plane, the peak shifts to higher binding energies. This substantiates a deterioration of the surface leading to the observed satellite structure in the O 1s core-level photoemission spectra of the cuprate superconductors.