As the alignment of a feed antenna to a steerable reflectarray becomes increasingly complicated at upper mm-wave frequencies, illuminating the structure from the far field is desirable. Simultaneously, the required fabrication precision makes large arrays expensive, effectively limiting the size. Consequently, spill-over feed radiation results in specular reflections, degrading the array's far-field pattern. To mitigate these undesired reflections, planar periodic structures can be employed to implement spatial filtering. Three designs that reduce specular reflections of a planar surface, caused by an obliquely-incident wave at 240 GHz, are proposed. Additional to standard evaluation of the absorptivity per unit cell, this paper examines the suppression mechanism by studying the scattered far field of size-limited structures. To verify each design, the frequency dependency of the specular reflection and the far-field pattern of a small array are measured. In accordance with simulations, two polarizationmaintaining variants feature 10 dB attenuation, whereas a modeconverting design achieves 23 dB.