1. Cut the grapefruit rinds into strips about 1/4-inch, or slightly less. (About .5cm.) Blanche the peels by putting them in a large, non-reactive pot. Cover with water and bring to a boil. Reduce heat and simmer for 10 minutes. Drain the peels, put them back in the pot, cover with water and bring to a boil. Let simmer for 2-3 minutes, then drain.
2. Place the peels back in the pot. Attach a candy thermometer to the side of the pot and add the 3 cups sugar, 2 1/2 cups water, and corn syrup. Cook over medium-high heat until the temperature reaches 225ºF (107ºC.) Turn off the heat and use a slotted spoon to transfer the grapefruit peels onto a wire cooling rack set over a baking sheet, separating the peels into a single layer, Let the peels sit overnight. (You can reserve the syrup and use it for sweetening iced tea or lemonade, or another purpose.) If you don’t have a wire rack, you can use a colander or mesh strainer set over a bowl, gently turning the peels several times, to help them drain.
3. The following day, put the remaining 3/4 cup sugar in a medium bowl. Working on batches, place a handful of the candied peels in the bowl of sugar and toss to coat them thoroughly. Using your hands, gently (but with determination) shake off the excess sugar. You want to avoid any clumps of sugar, if possible. Set the sugared peels on the cooling rack again, keeping them separate, and coat the remaining candied grapefruit peels with sugar, spreading them out on the wire rack. Let stand at room temperature a few hours to dry, before serving.