  We use the stellar fossil record to constrain the stellar metallicity
evolution and star-formation histories of the post-starburst (PSB) regions
within 45 local post-starburst galaxies from the MaNGA survey. The direct
measurement of the regions' stellar metallicity evolution is achieved by a new
two-step metallicity model that allows for stellar metallicity to change at the
peak of the starburst. We also employ a Gaussian process noise model that
accounts for correlated errors introduced by the observational data reduction
or inaccuracies in the models. We find that a majority of PSB regions (69% at
$>1\sigma$ significance) increased in stellar metallicity during the recent
starburst, with an average increase of 0.8 dex and a standard deviation of 0.4
dex. A much smaller fraction of PSBs are found to have remained constant (22%)
or declined in metallicity (9%, average decrease 0.4 dex, standard deviation
0.3 dex). The pre-burst metallicities of the PSB galaxies are in good agreement
with the mass-metallicity relation of local star-forming galaxies. These
results are consistent with hydrodynamic simulations, which suggest that
mergers between gas-rich galaxies are the primary formation mechanism of local
PSBs, and rapid metal recycling during the starburst outweighs the impact of
dilution by any gas inflows. The final mass-weighted metallicities of the PSB
galaxies are consistent with the mass-metallicity relation of local passive
galaxies. Our results suggest that rapid quenching following a merger-driven
starburst is entirely consistent with the observed gap between the stellar
mass-metallicity relations of local star-forming and passive galaxies.
