Receptors on the surface of cells initiate and regulate cell signaling processes and have been extensively studied because they form an important class of immune receptors, e.g., T-cell receptors, which bind to ligands that are anchored to other cells or surfaces, but remain poorly understood. The T-cell receptor-ligand complex spans 15 nanometers, while its phosphatase (a surface molecule that interacts with the receptor) spans 40 nanometers. This has been proposed to lead to size-based segregation that triggers signaling, but it is unclear whether the mechanochemistry supports such small-scale segregation. We present a nanometer-scale quantitative model that couples membrane elasticity with compressional resistance and lateral mobility of phosphatase. We find robust supradiffusive segregation of phosphatase from a single receptor-ligand complex. The model predicts a time-dependent tension on the complex leading to a nonlinear relationship between stressed and unstressed bond lifetimes, which could enhance the receptor’s ability to discriminate between similar ligands. This provides a mechanical source of ligand sensitivity, in contrast to biochemical sources of sensitivity that have been proposed previously.