I outline a possible scenario to explain the dramatic enhancement in tidal disruption event (TDE) rates observed in post-starburst/E+A galaxies. The rate enhancement can occur after massive clusters formed in a central starburst reach the black hole due to dynamical friction inspiral. The roughly 100 Myr timescale for this inspiral process sets the clock for the TDE rate enhancement. During their initial starburst phase when the star clusters are forming, these galaxies would appear as blue compact dwarfs (BCDs), while by the time the rate enhancement occurs, these objects are observed as post-starburst galaxies. This scenario explains both the timescale of the stellar populations observed in TDE hosts, as well as the concentrated light profiles observed in these galaxies, as they gradually fade from being BCDs to early type galaxies.