Using a vegetable peeler, strip the zest from the orange, lemon, and lime. Cut the zests into very thin 1 1/2-inch-long strips. Peel the citrus fruits using a sharp paring knife, making sure to remove all the bitter white pith. Working over a bowl, cut in between the membranes to release the sections; squeeze the juice from the membranes into the bowl.
Put the sugar in a nonreactive medium saucepan and cook over moderate heat, stirring with a wooden spoon, until a clear amber syrup forms, 3 to 4 minutes. Immediately add the citrus zests and stir constantly for 30 seconds, then stir in the citrus fruits and juices and cook for 30 seconds more. Add the cranberries and bring to a gentle boil. Cook, stirring occasionally, until the relish is jamlike, about 12 minutes. Remove from the heat and stir in the Grand Marnier. Let cool completely, then refrigerate.
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