The aim of this work is to characterize the mechanical parameters governing the in-plane behavior of human skin and, in particular, of a keloid-scar. We consider 2D hyperelastic bi-material model of a keloid and the surrounding healthy skin. The problem of finding the optimal model parameters that minimize the misfit between the model observations and the in vivo experimental measurements is solved using our in-house developed inverse solver that is based on the FEniCS finite element computational platform. The paper focuses on the model parameter sensitivity quantification with respect to the experimental measurements, such as the displacement field and reaction force measurements. The developed tools quantify the significance of different measurements on different model parameters and, in turn, give insight into a given model's ability to capture experimental measurements. Finally, an apriori estimate for the model parameter sensitivity is proposed that is independent of the actual measurements and that is defined in the whole computational domain. This estimate is primarily useful for the design of experiments, specifically, in localizing the optimal displacement field measurement sites for the maximum impact on model parameter inference.