  The mass-sheet degeneracy is a well-known problem in gravitational lensing
which limits our capability to infer astrophysical lens properties or
cosmological parameters from observations. As the number of gravitational wave
observations grows, detecting lensed events will become more likely, and to
assess how the mass-sheet degeneracy may affect them is crucial. Here we study
both analytically and numerically how the lensed waveforms are affected by the
mass-sheet degeneracy computing the amplification factor from the diffraction
integral. In particular, we differentiate between the geometrical optics, wave
optics and interference regimes, focusing on ground-based gravitational waves
detectors. In agreement with expectations of gravitational lensing of
electromagnetic radiation, we confirm how, in the geometrical optics scenario,
the mass-sheet degeneracy cannot be broken with only one lensed image. However,
we find that in the interference regime, and in part in the wave-optics regime,
the mass-sheet degeneracy can be broken with only one lensed waveform thanks to
the characteristic interference patterns of the signal. Finally, we quantify,
through template matching, how well the mass-sheet degeneracy can be broken. We
find that, within present GW detector sensitivities and considering signals as
strong as those which have been detected so far, the mass-sheet degeneracy can
lead to a $1\sigma$ uncertainty on the lens mass of $\sim 12\%$. With these
values the MSD might still be a problematic issue. But in case of signals with
higher signal-to-noise ratio, the uncertainty can drop to $\sim 2\%$, which is
less than the current indeterminacy achieved by dynamical mass measurements.
