Excited Si$^+$ and Fe$^+$ species are routinely observed in the host environment of gamma-ray burst (GRB) afterglows but are not commonly seen in other extragalactic locations. Their presence signals unusual properties in the gaseous environment of these GRB hosts that arise either as a result of the intense ionizing radiation of the afterglow or through collision excitation in a dense cloud. In particular, the photon pumping scenario has explicit expectations for temporal variation in the strength of the excited lines, owing to the decline in the ionizing flux of the GRB afterglow. We analyze afterglow spectra of GRB 020813 obtained in two epochs åisebox-0.5ex 16 hr apart and examine transitions from the first excited state of Fe$^+$ at J=7/2 in these two sets of data. We report a significant decline by at least a factor of 5 in the equivalent width of the Fe II łambda2396 transition, the strongest from the J=7/2 state. We perform a Monte Carlo analysis and determine that this temporal variation is present at more than 3 σ level of significance. This observation represents the first detection in the temporal variation of the excited Fe$^+$ states in the GRB host interstellar medium, a direct influence of the burst itself on its environment. We further estimate that the Fe$^+$ gas resides 50-100 pc from the afterglow, based on the afterglow light curve and the presence and absence of the excited Fe II łambda2396 in the two-epoch observations.