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 (~80pc) and is therefore thinner than the GRXE of stellar origin (scale height ~130pc). 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 (~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.