Herein, we report a platform to integrate customizable quantities of catechol units into polymers by reacting caffeic acid carbonic anhydride with polymers having pendant amine groups. Brush poly(ethylene glycol)–caffeamide (PEG–CAF) copolymers based on oligo(ethylene glycol)methyl ether methacrylate (OEGMA500) were obtained with a catechol content of approximately 30, 40, and 50 mol % (vs OEGMA content). Owing to the hydrophobicity of the introduced CAF groups, the catechol copolymers exhibited cloud points in the range of 23–46 °C and were used to fabricate thermoresponsive FeIII metal–phenolic network capsules. Polymers with the highest CAF content (50 mol %) proved most effective for attenuating reactive oxygen species levels in vitro, in co-cultured fibroblasts, and breast cancer cells, even in the presence of an exogenous oxidant source. The reported approach to synthesize customizable catechol materials could be generalized to other amine-functional polymers, with potential biomedical applications such as adhesives or stimuli-responsive drug delivery systems.