Slice off the ends of one Rangpur lime and place it on one of its flat ends. Using a sharp knife or vegetable peeler, remove the peel in strips about 1-inch wide. Leave behind as much white pith as possible. Repeat with the remaining fruit. Use a sharp knife to help peel off any extra pith or remaining patches of skin [from the flesh of the fruit]. It doesnâ€™t need to be perfect. Reserve the flesh of the fruit. Julienne the Rangpur lime peel by stacking 3 or 4 pieces on top of one another and slicing them thin. Place the julienned peel in your preserving pot and set aside. Now, slice the reserved fruit in half lengthwise and slice the half lengthwise again. Cut each quarter crosswise to form many small 1/8-inch-thick Rangpur lime triangles. Reserve the seeds as you go. Put the fruit slices in a medium-size nonreactive bowl as you work. Once the flesh is sliced, tie up the seeds in a square of cheesecloth or scrap of white tea towel. Add them to the preserving pot with the julienned peel and cover with the water. Bring to a boil, reduce heat to low, and simmer for 5 minutes. Remove from heat and pour in the sliced Rangpur lime fruit. Let cool to room temperature and refrigerate overnight.
[Before you start, remove the rangpur lime seed bundle from the preserving pot and give it a good squeeze into the mixture, then discard the seeds.] Add the sugar and, over high heat, bring to a boil that cannot be stirred down. Cook, stirring frequently, until it passes the plate test, about 18 minutes. Ladle into prepared half-pint jars, leaving 1/4-inch headspace. Remove air bubbles. Wipe rims. Place the lids on the jars and screw on the bands until they are fingertip tight. Process in a water-bath canner for 10 minutes, adjusting for altitude as needed. After 24 hours, check the seals. Label, date, and store out of direct sunlight without the bands for up to a year.