For the honey-lime syrup: Bring the honey, lime peel and 1 cup water to a boil in a small saucepan; cook until reduced slightly. Transfer the syrup to a container with a lid and refrigerate until cold, about 30 minutes. Remove the peel before using. (Makes about 1 1/3 cups; cover and refrigerate extra syrup for up to 1 week.)
For the white tea and rum cocktail: Combine the tea, rum, lime juice, 1/2 ounce of the honey-lime syrup and some ice cubes in a cocktail shaker. Shake for 10 seconds. Strain into a martini glass and serve straight-up. Float a lime slice on top.