  The first evidence of the gamma-ray emission from the quiescent Sun was found
in the archival EGRET data that was later confirmed by Fermi-LAT observations
with high significance. This emission is produced by Galactic cosmic rays (CRs)
penetrating the inner heliosphere and inter- acting with the solar atmosphere
and optical photons. The solar emission is characterized by two spatially and
spectrally distinct components: (i) disk emission due to the CR cascades in the
solar atmosphere, and (ii) spatially extended inverse Compton (IC) emission due
to the CR electrons scattering off of solar photons. The intensity of both
components associated with Galactic CRs anti-correlate with the level of the
solar activity being the brightest during solar minimum. In this paper we
discuss updates of the models of the IC component of the emission based on CR
measurements made at different levels of solar activity, and we make
predictions for e- ASTROGAM and AMEGO, proposed low-energy gamma-ray missions.
