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X-ray thermal emission is inherent in neutron-star and black-hole X-ray binary systems. Within these systems, it may reflect from optically thick matter, which will create characteristic observable X-ray spectro-polarimetric features. We computed rest-frame reflection spectra and the corresponding energy-dependent linear polarization degree and angle for (un)polarized single-temperature blackbody spectra impinging on a partially ionized, constant-density, optically thick slab. We used a combination of a Monte Carlo simulation that takes into account scattering, absorption, and spectral lines, and a radiative transfer pre-computation of the ionization structure of the slab in photo-ionization equilibrium without assuming a local thermodynamic equilibrium. We discuss the impact of the reflector's ionization and the incident spectral shape on the obtained energy dependence of polarization. For isotropic incident intensity and for parallel rather than perpendicular unidirectional illumination with respect to the slab normal direction, despite the presence of highly polarized absorption features and low-polarized spectral lines, an underlying scattering-induced increase of polarization degree with energy in mid to hard X-rays naturally arises due to multiple Compton-scattering energy shifts. Such a re-processing effect is particularly apparent in 2─8 keV for steep incident X-ray spectra reflecting from highly ionized and optically thick media. Integration of the resulting local reflection tables in specific large-scale reflection geometries occurring in X-ray binary systems, including relativistic effects, will be presented in a follow-up paper. Nonetheless, we anticipate that the obtained rest-frame energy-dependent features will imprint to the observed X-ray polarization; and they could contribute to the increase of the total polarization degree with energy in the 2─8 keV range observed in some accreting systems by the IXPE mission.