  We report the discovery of an extended emission line region (EELR) in MUSE
observations of Markarian 950, a nearby ($z=0.01628$) post-starburst (PSB)
galaxy that hosted the tidal disruption event (TDE) iPTF-16fnl. The EELR
requires a non-stellar ionizing continuum with a luminosity L$_{\rm ion, min}
\gtrsim 10^{43}$ erg s$^{-1}$, inconsistent with the current weak state
(L$_{\rm IR,AGN} < 2.5 \times 10^{42}$ erg s$^{-1}$) of the galactic nucleus.
The ionized gas has low velocity ($\sim$-50 km s$^{-1}$) and low turbulence
($\sigma_{\rm gas} \lesssim$ 50 km s$^{-1}$), and is kinematically decoupled
from the stellar motions, indicating that the gas kinematics are not AGN
driven. Markarian 950 is the third post-starburst 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 $\sim 10 \times$ higher than in other PSB galaxies. This suggests
that a gas-rich post-merger 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.
