To make the syrup, combine all the ingredients in a small saucepan. Place over medium heat and allow to heat until the sugar has dissolved. Turn up the heat and allow to simmer for 5 minutes. Remove from the heat then allow to cool completely.
To make the paloma, combine the grapefruit juice and tequila in a jug then pour in some of the ginger syrup. Taste as you go to ensure it doesn't get too sweet. Top up with soda water, to taste, then serve in glasses with ice and lemon/lime slices.