  We use the IllustrisTNG simulations to investigate the evolution of the
mass-metallicity relation (MZR) for star-forming cluster galaxies as a function
of the formation history of their cluster host. The simulations predict an
enhancement in the gas-phase metallicities of star-forming cluster galaxies
(10^9< M_star<10^10 M_sun) at z<1.0 in comparisons to field galaxies. This is
qualitatively consistent with observations. We find that the metallicity
enhancement of cluster galaxies appears prior to their infall into the central
cluster potential, indicating for the first time a systematic "chemical
pre-processing" signature for {\it infalling} cluster galaxies. Namely,
galaxies which will fall into a cluster by z=0 show a ~0.05 dex enhancement in
the MZR compared to field galaxies at z<0.5. Based on the inflow rate of gas
into cluster galaxies and its metallicity, we identify that the accretion of
pre-enriched gas is the key driver of the chemical evolution of such galaxies,
particularly in the stellar mass range (10^9< M_star<10^10 M_sun). We see
signatures of an environmental dependence of the ambient/inflowing gas
metallicity which extends well outside the nominal virial radius of clusters.
Our results motivate future observations looking for pre-enrichment signatures
in dense environments.
