Thermal-energy atom scattering at a surface under grazing incidence conditions is an innovative method for investigating dispersive atom-surface interactions with potential application in quantum sensing interferometry. The complete establishment of this technique requires a detailed peak analysis, which is yet to be achieved. We examine peak-width fluctuations in atomic and molecular beams diffracted by a grating under grazing incidence conditions. Careful measurements and analyses of the diffraction patterns of He atoms and D2 molecules from three square-wave gratings with different periods and radii of curvature enable the identification of factors influencing the peak-width variations as a function of incidence angle. The effects of macroscopic surface curvature, grating magnification, and beam emergence are substantial under these conditions but negligible for incidence angles close to the normal. Our results shed light on the phenomena occurring in grazing incidence thermal-energy atom scattering.