The superconducting density of states of the two-dimensional electron system at the interface exhibits broad quasiparticle peaks that are well described by the Dynes parameter . We measured in a wide range of temperatures and gate voltages using tunneling spectroscopy. exhibits a temperature dependence, with . We discuss several interpretations of and conclude that is an intrinsic parameter of the superconducting state that quantifies the effect of the pair-breaking processes in the superconductor. The strong temperature dependence at low temperatures rules out inelastic electron scattering and magnetic scattering as the origin of the pair breaking. We find that can be explained by interband scattering and by scattering in a superconductor with nodes in the order parameter.