Interactions between the Atlantic Meridional Overturning Circulation (AMOC) and the Greenland ice-sheet (GrIS), both considered major tipping elements in the Earth system, are critical for understanding their future evolution under anthropogenic climate change. As global warming progresses, the potential weakening of the AMOC raises concerns that meltwater from the disintegrating GrIS could trigger a complete AMOC shutdown. Here, we assess the processes and feedback mechanisms that may either accelerate or stabilize these two Earth system components under idealized future scenarios in an ice-sheet coupled Earth system model of intermediate complexity with perturbed parameter ensembles. Our findings indicate that, under a moderate idealized scenario (2×CO2,PI, corresponding to ~3 °C global mean warming), GrIS meltwater alone is unlikely to trigger an AMOC collapse. However, this risk increases with higher emissions. Notably, the delayed GrIS response to the warming results in peak meltwater fluxes entering the North Atlantic only when the AMOC is already in its recovery phase, thereby reducing the likelihood of collapse. Additionally, the system is further stabilized by the cooling induced by the thermal bipolar seesaw. This cooling is sufficiently strong that, in the event of a future AMOC collapse, GrIS melting would effectively cease for ~3 °C warming, and its disintegration would be substantially delayed even under higher warming levels. Nonetheless, rapid CO2 reduction remains essential to prevent irreversible state transitions of both the AMOC and GrIS.