We investigate the impact of the strength of the Atlantic Meridional Overturning Circulation (AMOC) at 26° N on the prediction of North Atlantic sea surface temperature anomalies (SSTAs) a season ahead. We test the dependence of sea surface temperate (SST) predictive skill in initialised hindcasts on the phase of the AMOC at 26°N, invoking a seesaw mechanism driven by AMOC fluctuations, with positive SSTAs north of 26° N and negative SSTAs south of 26° N after a strong AMOC and vice versa. We use initialised simulations with the MPI-ESM-MR (where MR is mixed resolution) seasonal prediction system. First, we use an assimilation experiment between 1979-2014 to confirm that the AMOC leads a SSTA dipole pattern in the tropical and subtropical North Atlantic, with the strongest AMOC fingerprints after 2-4 months. Going beyond previous studies, we find that the AMOC fingerprint has a seasonal dependence and is sensitive to the length of the observational window used, i.e. stronger over the last decade than for the entire time series back to 1979. We then use a set of ensemble hindcast simulations with 30 members, starting each February, May, August and November between 1982 and 2014. We compare the changes in skill between composites based on the AMOC phase a month prior to each start date to simulations without considering the AMOC phase and find subtle influence of the AMOC mechanism on seasonal SST prediction skill. We find higher subtropical SST hindcast skill at a 2-4-month lead time for June-July-August (JJA) SSTA composites based on the AMOC phase at May start dates than for the full time period. In other regions and seasons, we find a negligible impact of the AMOC seesaw mechanism on seasonal SST predictions due to atmospheric influence, calling for caution when considering such a mechanism. Our method shows that, for May start dates following strong AMOC phases, summer SST hindcast skill over the subtropics increases significantly compared to that of weak AMOC phases. This suggests that in the assessment of SST skill for a season ahead an eye should be kept on the initial AMOC state.