Gin and Mint Tea Cocktail

Bring 3 cups water to a simmer in a small saucepan. Remove from heat, add tea, and let steep 3 minutes. Strain through a fine-mesh sieve into a medium bowl, then return tea to saucepan. Add ginger, orange zest, sugar, and ½ cup mint; return to a simmer over medium heat, stirring occasionally to dissolve sugar. Let cool.
Strain tea syrup through a fine-mesh sieve into a pitcher, pressing on solids; discard solids. Stir in gin and lemon juice and chill until cold, about 1 hour.
Serve in rocks glasses filled with ice garnished with lemon wheels and mint sprigs.
Do Ahead: Cocktail can be made 4 hours ahead. Keep chilled.