We investigate the short pulse laser induced damage initiation mechanism on multilayer dielectric (MLD) pulse compression gratings. We report by means of scanning electron microscopy that damages initiate on the edge of the grating pillars opposite to the incoming wave. It demonstrates, at the scale of a grating line, the role of the electric field in the damage process but we also that grating pillars damage is also spatially modulated in the form of a periodic ripple pattern developing along the polarization direction.