We study the mass-metallicity relation for 19 members of a spectroscopically-confirmed protocluster in the COSMOS field at $z=2.2$ (CC2.2), and compare it with that of 24 similarly selected field galaxies at the same redshift. Both samples are $rm Halpha$ emitting sources, chosen from the HiZELS narrow-band survey, with metallicities derived from $rm N2 (frac{rm [NII] lambda 6584}{rm H alpha})$ line ratio. For the mass-matched samples of protocluster and field galaxies, we find that protocluster galaxies with $10^{9.9} rm M_odot leq M_* leq 10^{10.9} rm M_odot$ are metal deficient by $0.10 pm 0.04$ dex ($2.5sigma$ significance) compared to their coeval field galaxies. This metal deficiency is absent for low mass galaxies, $rm M_* < 10^{9.9} rm M_odot$. Moreover, relying on both SED-derived and $rm {Halpha}$ (corrected for dust extinction based on $rm {M_*}$) SFRs, we find no strong environmental dependence of SFR-$rm {M_*}$ relation, however, we are not able to rule out the existence of small dependence due to inherent uncertainties in both SFR estimators. The existence of $2.5sigma$ significant metal deficiency for massive protocluster galaxies favors a model in which funneling of the primordial cold gas through filaments dilutes the metal content of protoclusters at high redshifts ($z gtrsim 2$). At these redshifts, gas reservoirs in filaments are dense enough to cool down rapidly and fall into the potential well of the protocluster to lower the gas-phase metallicity of galaxies. Moreover, part of this metal deficiency could be originated from galaxy interactions which are more prevalent in dense environments.
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