The low-frequency dynamics of the globular protein beta -lactoglobulin has been investigated by inelastic neutron scattering, on both dry and D2O-hydrated samples. Both the dynamic structure factor and the density of states display an excess of vibrational modes with respect to the Debye level, with such an excess being reminiscent of the so-called boson peak. To establish which protein structural elements give origin to the anomalous peak, the samples were submitted to suitable H/D exchange procedures, which allowed us to highlight the following points: (i) in the dry samples, nonexchangeable, internal, hydrogens display a peal, at 3 meV; (ii) exchangeable, mainly external, hydrogens provide a further peak, which is shifted to lower frequencies and displays a stronger intensity per atom; (iii) in the hydrated samples, no frequency difference between the peaks of external and internal hydrogens is found, meanwhile the stronger scattering intensity due to external hydrogens is still observed. These results are discussed in the framework of a model ascribing the anomalous bump to interactions of acoustic phonons with density fluctuations domains and the effect of hydration on the protein dynamics is revisited.