An innovative information-theoretic tool, transfer entropy, has been applied to measure the possible information flow and sense between two real time series: the South Atlantic Anomaly (SAA) area extent at the Earth's surface and the Global Sea Level (GSL) rise anomalies for the last 300 years. This connection was previously suggested considering only the long term trend. Now we study the possibility of that this relation also happens in shorter scales. The new results seem to support again this hypothesis, with more information transferred from the SAA to the GSL anomalies, with about 90 % of confidence level. This could provide a new clue on the existence of a link between the geomagnetic field and the Earth's climate in the past.