The El Niño-Southern Oscillation (ENSO), the primary driver of year-to-year global climate variability, is known to influence the North Tropical Atlantic (NTA) sea surface temperature (SST), especially during boreal spring season. Focusing on statistical lead-lag relationships, previous studies have proposed that interannual NTA SST variability can also feed back on ENSO in a predictable manner. However, these studies did not properly account for ENSO's autocorrelation and the fact that the SST in the Atlantic and Pacific, as well as their interaction are seasonally modulated. This can lead to misinterpretations of causality and the spurious identification of Atlantic precursors for ENSO. Revisiting this issue under consideration of seasonality, time-varying ENSO frequency, and greenhouse warming, we demonstrate that the cross-correlation characteristics between NTA SST and ENSO, are consistent with a one-way Pacific to Atlantic forcing, even though the interpretation of lead-lag relationships may suggest otherwise.