The exoergic Eley-Rideal hydrogen recombination on graphite surfaces is known to produce vibrationally hot product molecules. Realistic quantum scattering calculations at normal incidence over a wide range of collision energies show that the degree of vibrational excitation of the reaction product is a steep decreasing function of the collision energy. This results in selective population of the lower-lying vibrational levels and gives rise to an oscillating structure in the total reaction cross-sections at high energies, which cannot be reproduced by classical and quasi-classical trajectory calculations. An analogous quantum structure appears in the total collision-induced desorption cross-sections and is assigned to selective population of the metastable states of the transient molecular hydrogen.