  We study the properties of tidal disruption event (TDE) host galaxies in the
context of a catalog of ~500,000 galaxies from the Sloan Digital Sky Survey. We
explore whether selection effects can account for the overrepresentation of
TDEs in E+A/post-starburst galaxies by creating matched galaxy samples.
Accounting for possible selection effects due to black hole (BH) mass, redshift
completeness, strong AGN presence, bulge colors, and surface brightness can
reduce the apparent overrepresentation of TDEs in E+A host galaxies by a factor
of ~4 (from ~$\times$100-190 to ~$\times$25-48), but cannot fully explain the
preference. We find that TDE host galaxies have atypical photometric properties
compared to similar, "typical" galaxies. In particular, TDE host galaxies tend
to live in or near the "green valley" between star-forming and passive
galaxies, and have bluer bulge colors ($\Delta (g-r) \approx 0.3$ mag), lower
half-light surface brightnesses (by ~1 mag/arcsec$^2$), higher Sersic indices
($\Delta n_{\rm g} \approx 3$), and higher bulge-to-total-light ratios ($\Delta
B/T \approx 0.5$) than galaxies with matched BH masses. We find that TDE host
galaxies appear more centrally concentrated and that all have high galaxy
Sersic indices and $B/T$ fractions---on average in the top 10% of galaxies of
the same BH mass---suggesting a higher nuclear stellar density. We identify a
region in Sersic index and BH mass parameter space that contains ~2% of our
reference catalog galaxies but $\ge\!60\%$ of TDE host galaxies. The unique
photometric properties of TDE host galaxies may be useful for selecting
candidate TDEs for spectroscopic follow-up observations in large transient
surveys.
