We study dissipation in palladium (Pd) nanomechanical resonators at low temperatures in the linear response regime. Metallic resonators have shown characteristic features of dissipation due to tunneling two-level systems (TLS). The system described here offers a unique tunability of the dissipation scenario by adsorbing hydrogen (H-2), which induces a compressive stress. The intrinsic stress is expected to alter TLS behavior. We find a sublinear similar to T-0.4 dependence of dissipation in a limited temperature regime. As seen in TLS dissipation scenarios, we find a logarithmic increase of frequency from the lowest temperatures till a characteristic temperature T-co is reached. In samples without H-2, T-co similar to 1K was seen, whereas with H-2 it is clearly reduced to similar to 700 mK. Based on standard TLS phenomena, we attribute this to enhanced phonon-TLS coupling in samples with compressive strain. We also find that with H-2 there is a saturation in low-temperature dissipation, which may possibly be due to super-radiant interaction between TLS and phonons. We discuss the data in the scope of TLS phenomena and similar data for other systems.