Atomic hydrogen (H) is supplied during Si capping (by solid source MBE at 400 degrees C) of Ge related islands strained on Si(001). Without H, Si capping is known to smooth the initial rough surface caused by the Stranski-Krastanov Ge growth mode which ensures a partial strain relief at the island crests. We demonstrate elsewhere that this smoothing takes place by stress mediated surface migration of Si accumulating in the troughs between the hut-clusters where the misfit is the lowest and by lateral Ge segregation. Similar to a growth temperature lowering which reduces these surface migrations, the effect of H is to maintain the stress induced roughening suppressed by Si, as proven by the persistence of spotty RHEED patterns and by the non-restoration of intensity oscillations. Moreover, the ali recovery of the Si bulk value in the Si cap layer is significantly slower than without H, a consequence of the kinetically blocked Si deposition, particularly on the top of the partially relaxed hut clusters where it is forced to grow more tensely strained than without H. As a general learning, the same H adsorption and relevant adatom mobility decrease is able to presently preserve the initial Ge related 3D growth whereas, for the growth of Ge upon Si, it maintains a 2D growth in preventing 3D island formation. In both cases of tensely or compressively strained growths, the H-induced kinetic diffusion length limitation impedes local elastic energy minimizing occurring, without H, by strain relieving adatom migrations. Additionally, the fact that the step density is here essentially unchanged by the growth under H, does not support the use of step involving models to explain the H-surfactant action.