Preheat oven to 350 degrees F (175 degrees C). Whisk flour, baking soda, and salt together in a bowl.
Mix 1 1/2 teaspoon of grapefruit juice into milk in a small bowl, and set aside for about 5 minutes. In a large bowl, mash the butter with 3/4 cup of sugar until creamy and well combined, and beat in the egg and grapefruit zest until thoroughly combined. Beat the milk into the butter mixture about 2 tablespoons at a time, alternating with the flour mixture, until the dough is smooth. Drop by teaspoons onto ungreased baking sheets, about 2 inches apart. Bake in the preheated oven until set and very lightly browned, 12 to 14 minutes. Cool on racks. Make glaze by mixing 3/4 cup sugar with 1/4 cup citrus tea. Brush glaze onto cooled cookies; let stand until glaze is set.