  Tidal Disruption Events (TDEs) are transient events observed when a star
passes close enough to a supermassive black hole to be tidally destroyed. Many
TDE candidates have been discovered in host galaxies whose spectra have weak or
no line emission yet strong Balmer line absorption, indicating a period of
intense star formation that has recently ended. As such, TDE host galaxies fall
into the rare class of quiescent Balmer-strong galaxies. Here, we quantify the
fraction of galaxies in the Sloan Digital Sky Survey (SDSS) with spectral
properties like those of TDE hosts, determining the extent to which TDEs are
over-represented in such galaxies. Galaxies whose spectra have Balmer
absorption H$\delta_{\rm A}$ $-$ $\sigma$(H$\delta_{\rm A}$) $>$ 4 \AA\ (where
$\sigma$(H$\delta_{\rm A}$) is the error in the Lick H$\delta_{\rm A}$ index)
and H$\alpha$ emission EW $<$ $3$ \AA\ have had a strong starburst in the last
$\sim$Gyr. They represent 0.2% of the local galaxy population, yet host 3 of 8
(37.5%) optical/UV-selected TDE candidates. A broader cut, H$\delta_{\rm A} >$
1.31 \AA\ and H$\alpha$ EW $<$ $3$ \AA, nets only 2.3% of SDSS galaxies, but 6
of 8 (75%) optical/UV TDE hosts. Thus, quiescent Balmer-strong galaxies are
over-represented among the TDE hosts by a factor of 33-190. The
high-energy-selected TDE Swift J1644 also lies in a galaxy with strong Balmer
lines and weak H$\alpha$ emission, implying a $>80\times$ enhancement in such
hosts and providing an observational link between the $\gamma$/X-ray-bright and
optical/UV-bright TDE classes.
