Electron-phonon coupling is central to many condensed matter phenomena. Harnessing these effects for functionality in materials always involves nonequilibrium electronic states, which in turn alter quasi-free-carrier density and screening. Thus, gaining a fundamental understanding of the interplay of carrier screening and electron-phonon coupling is essential for advancing ultrafast science. Prior work has mainly focused on the impact of carrier screening on electronic structure properties. Here, we investigate the nonequilibrium lattice dynamics of MoS