The last deglaciation offers valuable insights into ice-climate interactions, as extensive paleoclimatic records document the retreat of ice sheets through a period of major climate changes. During this interval, the Greenland Ice Sheet (GrIS) retreated from its extensive Last Glacial Maximum (LGM) configuration to its present state, passing through the Holocene Thermal Maximum (HTM), when temperatures exceeded present-day values. Despite the large amount of paleoclimatic data available, ice-sheet models struggle to reproduce key aspects of the observational record, and the magnitude of the GrIS contribution to sea level throughout this period, in particular during the LGM and the HTM, remains highly uncertain. In this study, we evaluate an ensemble of 3,000 simulations of the GrIS performed with the Yelmo ice-sheet model against different observational constraints. These include: (1) the LGM ice-sheet extent, (2) ice-core-derived surface elevations, (3) an ice-extent retreat chronology based on the recent PaleoGrIS dataset, and (4) the present-day ice-sheet configuration (ice thickness, ice cover, ice-surface velocity, and bedrock elevation). We characterize the impact of the parameters perturbed along the ensemble on the GrIS evolution using an emulator based on the XGBoost algorithm combined with the SHAP (SHapley Additive exPlanations) framework. This analysis reveals that the climatic parameters (surface melting corrections and ocean thermal sensitivity) dominate the impact. By identifying the simulation that best matches these observables, we provide a constrained reconstruction of the GrIS during the last deglaciation that substantially improves upon previous reconstructions. We obtain a GrIS contribution to global sea level with respect to present of -5.75 m of sea-level equivalent (SLE) at the LGM (with an uncertainty range of -3.93 to -6.31 m) and +0.45 m after the HTM warming (with an uncertainty range of 0.43 to 1.18 m). This is in the upper range of previously existing estimates, indicating a comparatively mid-to-high GrIS sensitivity to climate changes over the last deglaciation.