The Greenland Ice Sheet (GrIS) is a critical tipping element in our Earth system, whose complete melt would raise global-mean sea levels by over 7 m. Yet, the temperature thresholds for its disappearance and subsequent recovery remain uncertain. Here, we simulate the state of the GrIS under increasing and decreasing temperatures in transient and equilibrium simulations using, for the first time, a comprehensive Earth System Model coupled to an Ice Sheet Model (ISM) that explicitly considers ice sheet-climate feedbacks and interactions. Our simulations indicate that the present-day GrIS destabilizes and disintegrates under a global warming of 2.55 ± 0.15 °C above pre-industrial (PI) temperatures, corresponding to the model's equilibrium response of a sustained atmospheric CO₂ concentration (pCO₂) of 403.5 ± 3.5 ppm, once its volume declines to 87 % of its PI state. Feedbacks and interactions of the GrIS with the atmosphere and ocean cause hysteresis and prevent full regrowth unless temperatures fall 1.3 ± 0.1 °C below PI temperatures (equivalent to 227 ± 2.5 ppm pCO₂, which is substantially lower than previous estimates. These feedbacks also stabilize the GrIS at multiple intermediate states during regrowth, which remain stable even if subjected to warming. We also apply statistical early warning signals to our transient retreat and regrowth branch simulations to test whether the critical transitions can be predicted. These indicators detect GrIS destabilization, but not regrowth. Our results suggest that we have already crossed the critical pCO₂ threshold in our current climate: maintaining or increasing our present-day pCO₂ level in the long-term, triggers a practically irreversible loss of the GrIS. In our simulations, regrowth requires pCO₂ reductions far below PI levels sustained over a significantly longer period than the duration of the ice sheet retreat. This implies that full GrIS recovery is unlikely under realistic long-term carbon removal and stabilization pathways.