Considered here is a plasma grating generated by two counterpropagating short laser pulses. Because of the shortness of the laser pulses, the plasma dynamics are determined by only electrons, which respond to the ponderomotive pressure generated by the interacting laser fields. An electron grating cannot exist for longer than the inverse ion plasma frequency, and so because of the limited time of the ponderomotive pressure, both the life time and spatial extent of an electron grating are finite. When one of the short laser pulses is circularly polarized (propagating in the x direction with electric field vectors in the yz plane) and the other is linearly y-polarized, the electron grating is produced by the y components. Meanwhile, the z component is partially reflected, and only a fraction of it is transmitted. Thus, the finite plasma grating can either alter the polarization of the yz-polarized pulse or act as a pulse splitter. The present paper is focused on the reflection and transmission rates. The action of the density grating on the z component cannot be explained by the Bloch wave theory for infinite crystals, and instead a theory is developed based on four-wave mixing, which explains the transmission and reflection of the z component when interacting with a grating of finite extent.