The Mars rover Curiosity carries an instrument called ChemCam to determine the composition of the soil and rocks via laser-induced breakdown spectroscopy (LIBS). Los Alamos National Laboratory has developed a simulation capability that can predict spectra from ChemCam, but there are major-scale differences between the prediction and observation. This presents a challenge when using Bayesian model calibration to determine the unknown physical parameters that describe the LIBS observations. We present an analysis of LIBS data to support ChemCam based on including a structured discrepancy model in a Bayesian model-calibration scheme. This is both a novel application and an illustration of the importance of setting scientifically informed and constrained discrepancy models within Bayesian model calibration.