The shape and extent of the Greenland Ice Sheet (GIS) during the Last Interglacial (LIG) is a matter of controversy, with different studies proposing a wide range of reconstructions. Here, for the first time, we combine stable water isotopic information from ice cores with isotope-enabled climate model outputs to investigate the problem. Exploring the space of possible ice sheet geometries by simulation is prohibitively expensive. We address this problem by using a Gaussian process emulator as a statistical surrogate of the full climate model. The emulator is calibrated using the results of a small number of carefully chosen simulations and then permits fast, probabilistic predictions of the simulator outputs at untried inputs. The inputs are GIS morphologies, parameterized through a dimension-reduction technique adapted to the spherical geometry of the setting. Based on the emulator predictions, the characteristics of morphologies compatible with the available ice core measurements are explored, leading to a reduction in uncertainty on the LIG GIS morphology. Moreover, a scenario-based approach allows to assess the gains in uncertainty reduction which would result from the availability of better dated LIG measurements in Greenland ice cores.