Combine the jalapeño quarters, sugar and 1/2 cup water in a small saucepan and bring to a simmer over medium heat. Simmer for 2 minutes. Set aside to infuse for about 45 minutes, depending on how spicy you want the syrup. Strain and discard the jalapeños.
In a tall glass filled with ice, combine the mezcal, grapefruit juice and 1 ounce of the jalapeño syrup. Top off with the club soda. Give the drink a quick stir, then drop in the jalapeño slices and serve with a straw.
Refrigerate the extra jalapeño syrup in an airtight container and save for another use.