Aqueous polyelectrolytes are effective mineralization inhibitors due to their ability to template onto crystal surfaces and chelate ions in solution. These additives have been shown to alter the morphology of calcium carbonate crystals, making them promising candidates for biological and industrial applications. However, while key to designing more effective mineralization inhibitors, the molecular mechanisms governing the interactions between polyelectrolytes and crystal surfaces remain poorly understood. In this study, we investigate the adsorption of poly(acrylic acid) (PAA) on the dominant calcite cleavage plane using all-atom molecular dynamics simulations. Although the calcite slab is electrostatically neutral, its charge distribution induces a strong electrostatic potential in an aqueous solution, which leads to significant water structuring at the interface. We observe a very favorable adsorption affinity of the polyelectrolyte chain to the surface, yet the structure of the interfacial water is not significantly affected. Direct interactions between the monomers on the polyelectrolyte and the calcite surface are infrequent, despite variations in chain length, charge density of the polyelectrolyte, and solution conditions. Intriguingly, the polyelectrolyte interaction with the calcite surface is dominantly mediated through bridging hydrogen bond interactions. As the polyelectrolyte adsorbs to the surface, the chain conformation adapts to the interfacial water structure by increasing polyelectrolyte-water contacts and integrates into pre-existing hydrogen bond networks. We found that water-mediated interactions are more dominant than direct interactions between the polyelectrolyte and the surface. This suggests an alternative pathway to the widely accepted notion that entropic effects due to water reorganization are the primary driving force. These results suggest that the polyelectrolyte binding affinity can be tuned by altering the polymer chain interactions with the interfacial water structure in addition to the surface itself.