  We constrain the recent star formation histories of the host galaxies of
eight optical/UV-detected tidal disruption events (TDEs). Six hosts had quick
starbursts of <200 Myr duration that ended 10 to 1000 Myr ago, indicating that
TDEs arise at different times in their host's post-starburst evolution. If the
disrupted star formed in the burst or before, the post-burst age constrains its
mass, generally excluding O, most B, and highly massive A stars. If the
starburst arose from a galaxy merger, the time since the starburst began limits
the coalescence timescale and thus the merger mass ratio to more equal than
12:1 in most hosts. This uncommon ratio, if also that of the central
supermassive black hole (SMBH) binary, disfavors the scenario in which the TDE
rate is boosted by the binary but is insensitive to its mass ratio. The stellar
mass fraction created in the burst is 0.5-10% for most hosts, not enough to
explain the observed 30-200x boost in TDE rates, suggesting that the host's
core stellar concentration is more important. TDE hosts have stellar masses
10^9.4 - 10^10.3 Msun, consistent with the SDSS volume-corrected, quiescent
Balmer-strong comparison sample and implying SMBH masses of 10^5.5 - 10^7.5
Msun. Subtracting the host absorption line spectrum, we uncover emission lines;
at least five hosts have ionization sources inconsistent with star formation
that instead may be related to circumnuclear gas, merger shocks, or post-AGB
stars.
