We present results from the first public data release of the MaNGA-ARO Survey of CO Targets (MASCOT), focussing our study on galaxies whose star-formation rates and stellar masses place them below the ridge of the star-forming Main Sequence. In optically-selected type 2 AGN/LINERs/Composites, we find an empirical relation between gas-phase metallicity gradients ∇Z and global molecular gas depletion times $t_{\rm dep} = M_{\rm H_2} /{\rm SFR}$ with “more quenched” systems showing flatter/positive gradients. Our results are based on the O3N2 metallicity diagnostic (applied to star-forming regions within a given galaxy) which was recently suggested to also be robust against emission by diffuse ionised gas (DIG) and low-ionisation nuclear emission regions (LINERs). We conduct a systematic investigation into possible drivers of the observed ∇Z − tdep relation (ouflows, gas accretion, in-situ star formation, mergers, and morphology). We find a strong relation between ∇Z or tdep and centralised outflow strength traced by the [O iii] velocity broadening. We also find signatures of suppressed star-formation in the outskirts in AGN-like galaxies with long depletion times and an enhancement of metals in the outer regions. We find no evidence of inflows impacting the metallicity gradients, and none of our results are found to be significantly affected by merger activity or morphology. We thus conclude that the observed ∇Z − tdep relation may stem from a combination of metal redistribution via weak feedback, and a connection to in-situ star formation via a resolved mass-metallicity-SFR relation.