Place pineapple and ginger in medium bowl. Muddle mixture by using bottom of heavy measuring cup to press pineapple until crushed. Add turmeric; mix well.
Divide dandelion greens among 4 beverage glasses; muddle gently with a muddler or wooden spoon. Top each with 1/4 of the pineapple mixture.
Pack crushed ice into each glass. Top each with 1/2 cup grapefruit soda. Serve immediately.