A comprehensive study of free energy landscapes and mechanisms of COS-mediated polymerization of glycine via N-carboxy anhydrides (NCAs, "Leuchs anhydrides") and peptide hydrolysis at the water pyrite interface at extreme thermodynamic conditions is presented. Particular emphasis is set on the catalytic effects of the mineral surface including the putative role of the ubiquitous sulfur vacancy defects. It is found that the mere presence of a surface is able to change the free energetics of the elementary reaction steps. This effect can be understood in terms of a reduction of entropic contributions to the reactant state by immobilizing the reactants and/or screening them from bulk water in a purely geometric ("steric") sense. Additionally, the pyrite directly participates chemically in some of the reaction steps, thus changing the reaction mechanism qualitatively compared to the situation in bulk water. First, the adsorption of reactants on the surface can preform a product-like structure due to immobilizing and scaffolding them appropriately. Second, pyrite can act as a proton acceptor, thus replacing water in this role. Third, sulfur vacancies are found to increase the reactivity of the surface. The finding that the presence of pyrite speeds up the rate-determining step in the formation of peptides with respect to the situation in bulk solvent while stabilizing the produced peptide against hydrolysis is of particular interest to the hypothesis of prebiotic peptide formation at hydrothermal aqueous conditions. Apart from these implications, the generality of the studied organic reactions are of immediate relevance to many fields such as (bio)geochemistry, biomineralization, and environmental chemistry.