The Atlantic Meridional Overturning Circulation (AMOC) carries warm upper waters into northern high-latitudes and returns cold deep waters southward. Under anthropogenic greenhouse gas forcing the AMOC is expected to weaken due to high-latitude warming and freshening. Here, we show that the sensitivity of the AMOC to an impulsive forcing at high latitudes is an oscillatory function of forcing lead time. This leads to the counter-intuitive result that a stronger AMOC can emerge as a result of, although some years after, anomalous warming at high latitudes. In our model study, there is no simple one-to-one correspondence between buoyancy forcing anomalies and AMOC variations, which retain memory of surface buoyancy fluxes in the subpolar gyre for 15–20 years. These results make it challenging to detect secular change from short observational time series.