We have studied the optical transmission properties of a number of different dielectric diffraction gratings that each exhibit two-dimensional chirality in their grating elements. We have found that the diffracted beams transmitted through these structures exhibit large anisotropic polarization changes and polarization-dependent intensity modulations even though the chiral elements are arranged in square grating arrays. The strength and functional form of both of these effects differ for each diffracted beam. They are also dependent on the chirality of the surface patterning and the thickness of the patterned dielectric film. We show how these properties could be exploited to provide a new and more versatile form of polarimeter, and how the operation of such a device is inherently dependent on the optical non-reciprocity of these chiral gratings.