Remove a 1-1/2 1-inch strip of peel from one of the oranges; set oranges aside. In a small saucepan, combine the strip of orange peel, the cranberries, brown sugar, the water, orange juice, and the 1 star anise. Bring to boiling; reduce heat. Simmer, uncovered, for 5 minutes, stirring occasionally. Transfer cranberry mixture to a medium bowl. Cool slightly. Discard orange peel and anise.
Meanwhile, peel, seed, and section the oranges and the grapefruit over a small bowl to catch juices. Stir orange and grapefruit sections and juices into the cranberry mixture.
Serve compote warm or chilled. If desired, garnish with additional star anise (do not eat the garnish).