Climate model simulations that restore SSTs in the North Atlantic have been used to explore the climate impacts of Atlantic Multidecadal Variability (AMV). However, despite simulations and observations exhibiting similar North Atlantic SST anomalies, experiments with active SST-restoring in the Tropical North Atlantic exhibit strong positive surface heat-fluxes out of the ocean with warm SST anomalies, which is not replicated in other simulations or observations. The upward surface heat-fluxes that are systematically driven by the active SST-restoring in the Tropical North Atlantic are found to be crucial for generating a strong local precipitation response and the associated remote impact on the Pacific Walker circulation; these are both absent in other simulations. The results of this study strongly suggest that experiments employing SST-restoring (or prescribed SSTs) in the Tropical North Atlantic exaggerate the influence of the Atlantic on patterns of global climate anomalies and its role in recent multidecadal SST trends.