In the sub-polar North Atlantic, the accumulation of fresh meltwaters from Greenland and the Arctic can impact the strength of the climatically important Atlantic Meridional Overturning Circulation. In this study I pin down the role of eddies in transporting these freshwaters away from their sources and identify connections between the accumulation, destruction and import of low-salinity waters around the coast of Greenland. I use ten years of daily outputs from the coupled ICON general circulation model, run with a 10~km atmosphere and a 5~km (eddy resolving) ocean. Comparing transports of low-salinity waters with traditionally defined freshwater transports, I find freshwater transports around Greenland do not describe pathways of low-salinity waters. Offshore transports of freshwater are often found to result from onshore transports of saline water, with low-salinity waters remaining confined to the Greenland shelf. Across shelf exchanges are relatively weak around the East Coast and become appreciable only on the Western coast. Eddy transports of low-salinity waters are weak apart from on the West Coast of Greenland and near Denmark Strait during wintertime. Balances between the import of low-salinity waters, their storage and their destruction via mixing vary depending upon both the season and region in question, implying that where and when freshwater is input around Greenland will affect both its salinity and the time elapsed upon its eventual arrival in the Labrador Sea.