In a small saucepan, stir 1 cup water, the sugar and thyme sprigs over medium-high heat. Bring to a boil, then reduce the heat and simmer until the sugar dissolves, 3 to 5 minutes. Remove the syrup from the heat and discard the thyme.
Add the grapefruit juice, vodka and simple syrup to a pitcher. Add in the grapefruit and the ice, and stir. Pour the cocktail over ice to serve.
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