To infuse the gin with tea: Put the gin and earl grey tea in a non-reactive container; stir to combine. Cover and set aside to steep for 1 hour. Strain without pressing down the leaves. The infused gin will keep, covered, for up to 3 weeks.
Whisk the egg white powder and warm water in a small bowl until smooth and frothy. Fill a cocktail shaker two-thirds full of ice and add 1 1/2 ounces of the infused gin, lemon juice, simple syrup, and egg white mixture. Cover and shake vigorously until thoroughly mixed and chilled, about 30 seconds. (In general, the drink is ready by the time the shaker mists up.) Fill the bottom of a martini glass with maraschino syrup. Strain cocktail into the glass to float on top of syrup. Drop in the lemon twist. Drink.
Put the sugar and water in a small saucepan. Cook over low heat, stirring, until the sugar dissolves. (Alternatively, heat in the microwave.) Let come to room temperature and store in a sealed container in the refrigerator for up to a month.