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In 1T-TaS₂, it is known that an electron-phonon-driven charge density wave precedes a Mott insulating ground state, but much about the nature of each of these phenomena has yet to be established. Fresh insights may be gained from observing the dynamics of the coupled lattice and charge degrees of freedom. Here, we observe the dynamic response to tunneling injection of single electrons, facilitated using a scanning tunneling microscope. This reveals unusual narrow electronic excitations at the upper Hubbard band onset, and their apparent electron-phonon replicas. The replicas likely stem from excitation of amplitude mode phonons associated with the 'Star-of-David' charge density wave. The narrow electronic excitations themselves may hint at coherent quasiparticles, polaronic bound states, or an as yet unknown phenomenon of strongly correlated and electron-phonon coupled systems. These observations may extend our microscopic understanding of systems in which electronic correlations and electron-phonon coupling are both strong, and should spur a new theoretical push to understand the excitations which arise.