  From a large sample of $\approx 170,000$ local SDSS galaxies, we find that
the Fundamental Metallicity Relation (FMR) has an overabundance of outliers,
compared to what would be expected from a Gaussian distribution of residuals,
with significantly lower metallicities than predicted from their stellar mass
and star formation rate (SFR). This low-metallicity population has lower
stellar masses, bimodial specific SFRs with enhanced star formation within the
aperture and smaller half-light radii than the general sample, and is hence a
physically distinct population. We show that they are consistent with being
galaxies that are merging or have recently merged with a satellite galaxy. In
this scenario, low-metallicity gas flows in from large radii, diluting the
metallicity of star-forming regions and enhancing the specific SFR until the
inflowing gas is processed and the metallicity has recovered. We introduce a
simple model in which mergers with a mass ratio larger than a minimum dilute
the central galaxy's metallicity by an amount that is proportional to the
stellar mass ratio for a constant time, and show that it provides an excellent
fit to the distribution of FMR residuals. We find the dilution time-scale to be
$\tau=1.568_{-0.027}^{+0.029}$ Gyr, the average metallicity depression caused
by a 1:1 merger to be $\alpha=0.2480_{-0.0020}^{+0.0017}$ dex and the minimum
mass ratio merger that can be discerned from the intrinsic Gaussian scatter in
the FMR to be $\xi_\text{min}=0.2030_{-0.0095}^{+0.0127}$ (these are
statistical errors only). From this we derive that the average metallicity
depression caused by a merger with mass ratio between 1:5 and 1:1 is 0.114 dex.
