Abstract We report the discovery of an extended emission-line region (EELR) in MUSE observations of Markarian 950, a nearby ( z = 0.01628) poststarburst (PSB) galaxy that hosted the tidal disruption event (TDE) iPTF 16fnl. The EELR requires a nonstellar ionizing continuum with a luminosity L ion , min ≳ 10 43 erg s −1 , inconsistent with the current weak state ( L IR,AGN < 2.5 × 10 42 erg s −1 ) of the galactic nucleus. The ionized gas has low velocity (∼–50 km s −1 ) and low turbulence ( σ gas ≲ 50 km s −1 ) and is kinematically decoupled from the stellar motions, indicating that the gas kinematics is not active galactic nucleus (AGN) driven. Markarian 950 is the third PSB galaxy to host a weak nuclear ionizing source as well as an EELR and a TDE. The overall properties of these three galaxies, including the kinematics and accretion history, are unusual but strikingly similar. We estimate that the incidence of EELRs in PSB-TDE hosts is a factor of ∼10 × higher than in other PSB galaxies. This suggests that a gas-rich postmerger environment is a key ingredient in driving elevated TDE rates. Based on the current observations, we cannot rule out that the EELRs may be powered through an elevated TDE rate in these galaxies. If the EELRs are not TDE powered, the presence of intermittent AGN activity, and in particular the fading of the AGN, may be associated with an increased TDE rate and/or an increased rate of detecting TDEs.