Martensite is a major constituent of Fe-C alloys. Its metastable body-centered tetragonal structure provides high tensile strength to martensitic steels. Recent experiments highlighted the benefit of large solute carbon content to the strength and ductility of the so-called virgin martensite obtained by sub-zero quench. The results suggest a significant contribution of the elastic and anelastic deformation of the martensite crystals to the rheology of these alloys. In order to shed light on the influence of carbon content on the anelastic response, we investigated theoretically the behavior of solute carbon during Snoek relaxation. Thanks to a linear-response approach, we obtained analytical formulae of the atomic mobilities and the thermodynamic affinities, from which the relaxation strength and time were derived. We unravel the unexpected decrease of the relaxation strength and time when solute carbon content is increased. Relaxation kinetics is explained at the atomic scale by an indirect mechanism of carbon migration in martensite, at variance with ferrite. We emphasize the onset of non-linear effects when the applied stress is high.