The difference between North Atlantic subpolar gyre sea surface temperatures (SPG SSTs) and hemispheric- or global-scale surface temperatures has been utilized as an index of centennial-timescale changes in Atlantic Meridional Overturning Circulation (AMOC) strength. Here, using Community Earth System Model ensembles, we show that surface temperature-based indices (STIs) proposed to date largely reflect global-scale temperature trends and thus do not reflect dynamical relationships with AMOC. More broadly, we find that relationships between STIs, SPG SSTs, and AMOC strength differ greatly in significance and magnitude over different time periods because they are dependent upon the nature of external forcing. In the 20th century, characterized by offsetting greenhouse gas and aerosol forcing, the relationship between SSTs and AMOC strength varies widely and changes sign across a 20-member ensemble. We conclude that STIs and SPG SSTs are poor predictors of centennial-timescale AMOC strength variations.