You don't pay a rope to leave land, so neither do you pay it to enter.
Unless you're going over pack ice, of course. You always need to use rope to cross pack ice. If you're crossing it when you jump in the water, leave the rope on the floe you jumped from and put your fish in the supply. Now that you're in the water, you need to get on another floe. This costs nothing if you can do it by crossing a flat edge. But again, if you need to cross pack ice, you need to use rope. In this case, you're in the water when you use the rope, so it goes back to the general supply.