We predict a thin diffuse component of the Galactic Ridge X-ray emission ( GRXE ) arising from the scattering of the radiation of bright X-ray binaries ( XBs ) by the interstellar medium . This scattered component has the same scale height as that of the gaseous disk ( \sim 80 pc ) and is therefore thinner than the GRXE of stellar origin ( scale height \sim 130 pc ) . The morphology of the scattered component is furthermore expected to trace the clumpy molecular and HI clouds . We calculate this contribution to the GRXE from known Galactic XBs assuming that they are all persistent . The known XBs sample is incomplete , however , because it is flux limited and spans the lifetime of X-ray astronomy ( \sim 50 years ) , which is very short compared with the characteristic time of 1000-10000 years that would have contributed to the diffuse emission observed today due to time delays . We therefore also use a simulated sample of sources , to estimate the diffuse emission we should expect in an optimistic case assuming that the X-ray luminosity of our Galaxy is on average similar to that of other galaxies . In the calculations we also take into account the enhancement of the total scattering cross-section due to coherence effects in the elastic scattering from multi-electron atoms and molecules . This scattered emission can be distinguished from the contribution of low X-ray luminosity stars by the presence of narrow fluorescent K- \alpha lines of Fe , Si , and other abundant elements present in the interstellar medium and by directly resolving the contribution of low X-ray luminosity stars . We find that within 1 ^ { \circ } latitude of the Galactic plane the scattered emission contributes on average 10 - 30 \% of the GRXE flux in the case of known sources and over 50 \% in the case of simulated sources . In the latter case , the scattered component is found to even dominate the stellar emission in certain parts of the Galactic plane . X-rays with energies \gtrsim 1 keV from XBs should also penetrate deep inside the HI and molecular clouds , where they are absorbed and heat the interstellar medium . We find that this heating rate dominates the heating by cosmic rays ( assuming a solar neighborhood energy density ) in a considerable part of the Galaxy .