Add the teabags to a large tempered-glass pitcher and fill it three-quarters full with hot water.
Allow the tea to steep for three minutes, and remove the tea bags.
Add the sugar or sweetener.
Once the sugar has dissolved, add the lime juice.
Pour in one cup of white rum or more or less to taste.
Allow the mixture to cool in the fridge for several hours or overnight.
Garnish with ice, a fresh lemon slice, and mint leaves before serving.