This study focused on the efficacy of a calcined layered double hydroxide (CLDH) clay in adsorbing two antiretroviral drugs (ARVDs), namely efavirenz (EFV) and nevirapine (NVP), from wastewater. The clay was synthesized using the co-precipitation method, followed by subsequent calcination in a muffle furnace at 500 °C for 4 h. The neat and calcined clay samples were subjected to various characterization techniques to elucidate their physical and chemical properties. Response surface modelling (RSM) was used to evaluate the interactions between the solution’s initial pH, adsorbent loading, reaction temperature, and initial pollutant concentration. Additionally, the adsorption kinetics, thermodynamics, and reusability of the adsorbent were evaluated. The results demonstrated that NVP exhibited a faster adsorption rate than EFV, with both reaching equilibrium within 20–24 h. The pseudo-second order (PSO) model provided a good fit for the kinetics data. Thermodynamics analysis revealed that the adsorption process was spontaneous and exothermic, predominantly governed by physisorption interactions. The adsorption isotherms followed the Freundlich model, and the maximum adsorption capacities for EFV and NVP were established to be 2.73 mg/g and 2.93 mg/g, respectively. Evaluation of the adsorption mechanism through computational analysis demonstrated that both NVP and EFV formed stable complexes with CLDH, with NVP exhibiting a higher affinity. The associated adsorption energies were established to be −731.78 kcal/mol for NVP and −512.6 kcal/mol for EFV. Visualized non-covalent interaction (NCI) graphs indicated that hydrogen bonding played a significant role in ARVDs-CLDH interactions, further emphasizing physisorption as the dominant adsorption mechanism.