In a large bowl steep the tea bags with the boiling water and honey for 10 minutes. Remove the tea bags, mix well, and add enough cold water to make 4 cups. Set aside.

Cut the pith from the center of each lemon quarter and remove any seeds.

In a food processor combine the lemons (unpeeled), sugar, mint, and rum. Process until smooth, about 2 minutes.

Press the lemon mixture through a fine mesh sieve, catching the liquid in a bowl.

Add enough cold water to the lemonade to make 4 cups.

Combine the lemonade and iced tea in a pitcher and mix well. Refrigerate for at least 2 hours.

When ready to serve fill a glass with ice and pour the iced tea lemonade over top of it. Serve with a straw and a lemon wedge.