A new mechanism that degrades the temporal contrast of pulses generated in optical parametric chirped-pulse amplification (OPCPA) systems is presented in this paper. Post-pulses exist in any laser system, including pump lasers. When a CPA scheme is used for pumping, a small-scale modulation of the pump signal may arise from the interference of a post-pulse with the main chirped pump pulse; the pre-pulses appear in the signal when the pump interacts with the signal, and following recompression. An OPCPA system was modelled using numerical methods to study this phenomenon. It is shown that several pre- and post-pulses appear in the signal after recompression, leading to contrast degradation. The contrast of the recompressed signal is proportional to the contrast of the pump, and depends on the time delay of the post-pulse. The temporal positions of the pre- and post-pulses are also affected by the pump parameters.