Preheat a grill or grill pan to medium-high heat.
Slice the grapefruit in half horizontally and lightly brush the cut sides with oil to prevent sticking.
Place the grapefruit halves, cut side down, on the grill and cook for 4-5 minutes, or until grill marks appear and the fruit is slightly softened.
Remove the grapefruit from the grill and let cool slightly before juicing.
Once the grilled grapefruit halves have cooled, juice them using a citrus juicer or reamer. Strain the juice to remove any pulp or seeds.
Rim a highball glass with salt (optional) by running a lime wedge around the rim and dipping it into salt.
Fill the glass with ice cubes.
In a cocktail shaker, combine the tequila, fresh lime juice, agave syrup, and 2 ounces of grilled grapefruit juice. Add ice to the shaker and shake vigorously for about 15 seconds to chill the mixture.
Strain the shaken cocktail into the prepared glass filled with ice.
Top off the drink with grapefruit soda, leaving some room at the top of the glass.
Gently stir to combine the ingredients.
Garnish the cocktail with a grapefruit or lime wedge.
Serve immediately and enjoy the smoky and refreshing flavors of the grilled grapefruit paloma!