  The authors of Ref.[1] (referred to here as "Moskal et al.") claim to have
performed the most precise test of P, T and CP invariance in the decay of
ortho-Positronium. In this note: 1) we demonstrate, assuming standard
properties for Compton scattering, that the average value of the correlation
measured by Moskal et al. must necessarily be zero, independently of any
physics occurring in o-Ps decay; 2) we point out that there is no formal
justification to equate the normal vector to the Compton scattering plane with
the incident photon polarization, as done by Moskal et al.; 3) we observe the
absence of characterization of the device as a Compton polarimeter, which is
paramount in photon polarimetry; 4) we review previous measurements of the
polarization of photons from o-Ps decay, properly implementing the Compton
polarimetry technique, and make the connection with tests of discrete
symmetries; and 5) we stress that the correlation proposed by Moskal et al.
cannot be generated solely by the physics of o-Ps decay, including possible
violations of discrete symmetries.
