The release of contaminants of emerging concern (CECs) from the effluents of municipal wastewater treatment plants (MWWTPs) into the environment is a major problem because of its influence on both the environment and human health. The Fenton system has been demonstrated to remove CECs from different aqueous matrices effectively. However, the Fenton system has been considered to be efficient at acidic pH, which hinders its application in MWWTPs. Herein, the Fenton-like oxidation catalyzed by iron species intercalated between carbon layers of graphite (as a recyclable catalyst) was studied to remove amoxicillin, as a model pharmaceutical, from effluents of MWWTPs. Response surface methodology (RSM) was used to optimize system parameters, including catalyst loading, peroxydisulfate (PDS) dosage, and reaction time. Amoxicillin removal in the proposed system reached more than 99% by utilizing a catalyst dosage of 2 g/L and 5 mM of PDS at neutral pH. Sensitivity analysis of model parameters indicated that the amoxicillin removal was highly sensitive to the dosage of the catalyst, while the model is less sensitive to PDS dosage and reaction time. The results indicated that the PDS activation employing magnetic graphite intercalation compounds could be used as a promising system for pharmaceutical removal from MWWTP effluents.