Asteroseismology has become an increasingly relevant way to determine the global properties of stars and peer into their inner structure, both through advances in the observational and theoretical front. Our work takes us to its observational frontier by focusing on ε Indi, the coolest dwarf for which asteroseismic modes have so far been detected; and, from a theoretical perspective, performs a detailed study of stellar and asteroseismic modeling. We focus on the surface term, a systematic error in the oscillation frequencies between models and observations. To do this, we generated over 2,000 stellar tracks until the end of the main sequence using the stellar evolution code MESA, computing asteroseismic modes for each model with GYRE. We then performed model optimization with AIMS by comparing our grid of models with the observations for ε Indi, making use of the different prescriptions for the surface-term correction available to us. We investigated the impact that the different choices of model physics, such as the atmosphere and convective efficiency, can have on the mode frequencies. We find that the different surface-term corrections give consistent results with respect to the model optimization.