Environment plays a crucial role in shaping galaxy formation, yet the impact of overdensities on the internal chemical structure of galaxies at cosmic noon is still under debate. Here, we present spatially resolved gas-phase metallicity gradients for 42 star-forming galaxies in three massive protoclusters at $z \sim 2.3$, derived fromHubble Space Telescope (HST) slitless grism spectroscopy from the MAMMOTH-Grism survey. We find that the majority (29 of 42, $\sim$69%) of these protocluster members exhibit positive (inverted) metallicity gradients, a fraction significantly higher than observed in field galaxies of similar mass and redshift. By examining correlations with global properties, we show that these positive gradients are strongly associated with galaxies that are metal-deficient relative to the field mass-metallicity relation, particularly among the massive population ($\log(M_*/M_\odot) > 9.95$). These trends suggest that galaxies in dense protocluster environments experience substantial, enhanced inflows of pristine gas toward their central regions, which dilute the central metallicity and produce the observed inverted gradients. Our results provide observational evidence that environmental effects actively regulate gas accretion and chemical redistribution during the peak epoch of cosmic star formation.