A synchrotron-based scanning X-ray diffraction study on a GaP/Si pseudo-substrate is reported, within the context of the monolithic integration of photonics on silicon. Two-dimensional real-space mappings of local lattice tilt and in-plane strain from the scattering spot distributions are measured on a 200 nm partially relaxed GaP layer grown epitaxially on an Si(001) substrate, using an advanced sub-micrometre X-ray diffraction microscopy technique (K-Map). Cross-hatch-like patterns are observed in both the local tilt mappings and the in-plane strain mappings. The origin of the in-plane local strain variation is proposed to be a result of misfit dislocations, according to a comparison between in-plane strain mappings and transmission electron microscopy observations. Finally, the relationship between the in-plane strain and the free surface roughness is also discussed using a statistical method.