Nanoparticles with grafted layers of ligand molecules behave as soft colloids when they adsorb at fluid-fluid interfaces. The ligand brush can deform and reconfigure, adopting a lens-shaped configuration at the interface. This behavior strongly affects the interactions between soft nanoparticles at fluid-fluid interfaces, which have proven challenging to probe experimentally. We measure the surface pressure for a stable 2D interfacial suspension of nanoparticles grafted with ligands, and extract the interaction potential from these data by comparison to Brownian dynamics simulations. A soft repulsive potential with an exponential form accurately reproduces the measured surface pressure data. A more realistic interaction potential model is also fitted to the data to provide insights into the ligand configuration at the interface. The stress of the 2D interfacial suspension upon step compression exhibits a single relaxation time scale, which is also attributable to ligand reconfiguration.