Combine the sugar, water and mint leaves in a small saucepan. Heat on the stove top over low heat until the sugar has dissolved and the mint has infused the syrup, about 10 minutes. Strain and cool.
In a large pitcher add the tea, grapefruit juice and mint syrup. Serve chilled over ice and garnish each glass with a sprig of mint. Add the rum to the pitcher, if desired.