Dimension-5 photon (γ) scalar (φ) interaction term usually appear in the Lagrangians of bosonic sector of unified theories of electromagnetism and gravity. This interaction makes the medium dichoric and induces optical activity. Considering a toy model of an ultra-cold magnetized compact star ( White Dwarf (WD) or Neutron Star (NS)), we have modeled the propagation of very low energy photons with such interaction, in the environment of these stars. Assuming synchro-curvature process as the dominant mechanism of emission in such environments, we have tried to understand the polarimetric implications of photon-scalar coupling on the produced spectrum of the same. Further more assuming the 'emission-energy vs emission-altitude' relation, that is believed to hold in such (i.e. cold magnetized WD or NS) environments, we have tried to point out the possible modifications to the radiation spectrum when the same is incorporated along with dim-5 photon scalar mixing operator.