Rinse grapes and snip into small clusters, leaving stems attached. Pack grapes and star anise pods into a 1-qt. heat-resistant glass measuring cup or a wide-mouthed jar.
Combine remaining ingredients in a medium saucepan over high heat and bring to a boil. Heat until sugar dissolves, about 3 minutes; remove from heat and pour liquid over grapes. Let cool, then set a small saucer on top and a weight, if needed, to keep grapes immersed. Chill 2 to 3 days, depending on size (larger grapes take longer to pickle).