  We present MUSE integral field spectroscopic observations of the host galaxy
(PGC 043234) of one of the closest ($z=0.0206$, $D\simeq 90$ Mpc) and
best-studied tidal disruption events (TDE), ASASSN-14li. The MUSE integral
field data reveal asymmetric and filamentary structures that extend up to
$\gtrsim 10$ kpc from the post-starburst host galaxy of ASASSN-14li. The
structures are traced only through the strong nebular [O III] $\lambda$5007, [N
II] $\lambda$6584, and H$\alpha$ emission lines. The total off nuclear [O III]
$\lambda$5007 luminosity is luminosity is $4.7\times 10^{39}$ erg s$^{-1}$ and
the ionized H mass is $\rm \sim 10^4(500/n_e)\,M_{\odot}$. Based on the BPT
diagram, the nebular emission can be driven by either AGN photoionization or
shock excitation, with AGN photoionization favored given the narrow intrinsic
line widths. The emission line ratios and spatial distribution strongly
resemble ionization nebulae around fading AGNs such as IC 2497 (Hanny's
Voorwerp) and ionization "cones" around Seyfert 2 nuclei. The morphology of the
emission line filaments strongly suggest that PGC 043234 is a recent merger,
which likely triggered a strong starburst and AGN activity leading to the
post-starburst spectral signatures and the extended nebular emission line
features we see today. We briefly discuss the implications of these
observations in the context of the strongly enhanced TDE rates observed in
post-starburst galaxies and their connection to enhanced theoretical TDE rates
produced by supermassive black-hole binaries.
