In past global dust storms, no long lasting anomalies in the pressure cycle had been observed. The Global Dust Storm of Mars Year 34 (MY34), however, left behind an average surface pressure lower than what was expected based on the the values recorded on previous years by the Rover Environmental Monitoring Station (REMS) on Curiosity. The main signal contribution to the daily average surface pressure is the CO2 cycle, which is controlled by the Polar ice sublimation and freezing cycles. We used REMS and Mars Climate Sounder (MCS) data to search for correlations between the REMS anomaly and anomalies in the circulation compared to MCS observations from previous years. The findings include an early start of the retreat season for the Northern Polar cap, followed by the longest period of growth for the Southern Polar (SP) cap ice expansion since Curiosity had landed and then, during the dust storm, the longest retreat season of the Southern Polar cap. We also find a larger Northern Polar Cap extension after the storm, suggestive of a larger deposition of CO2 ice. The changes in length of the SP growth and retreat seasons might be consequence of the response of the zonal mean circulation to the dust storm. Changes in the structure of the zonal mean circulation compared to previous years are found in MCS data and presented. The combination of these anomalies constraint what physical processes may have caused this response in surface pressure after the dust storm.