Place the tea bag(s) in an iced tea jar or large pitcher. Pour the boiling water over the tea bag and let steep for at least 5 minutes.
While tea steeps, muddle the limes and the sugar in a medium bowl, until the sugar dissolves and the lime releases its juice.
After steeping, remove tea bags from the jar. Carefully add the lime/sugar mixture using a large spoon. Stir well to combine. Add the pomegranate juice and chill for at least 1 hour.
Just before serving, add the rum and stir to incorporate. Serve over ice.