Gently warm the agave syrup in a small saucepan just until fluid, never boiling, then remove from heat, add the grapefruit peel strips, cover, and let infuse for 20–30 minutes until aromatic and lightly bitter; strain out the peels and let the syrup cool completely.
Rub a lime wedge around the rims of the glasses, dip into coarse sea salt, and set aside; the rim should be assertive but clean, not crusted.
In a cocktail shaker, combine the blood orange juice, red grapefruit juice, lime juice, grapefruit-infused agave syrup, and the pinch of fine sea salt, then add plenty of ice and shake hard for 10–12 seconds to fully integrate acids, oils, and sweetness.
Strain the shaken base into a large pitcher or directly into the prepared glasses over fresh ice, top gently with chilled club soda, and stir once or twice only to integrate without flattening the bubbles.
Garnish with lime slices and twists of blood orange peel and serve immediately while cold, sharp, and lively.
