Preheat the oven to 350° F (180° C) and line a 9x5-inch loaf pan with parchment paper.
First, mix the dry ingredients. In a medium bowl, add the flour, baking powder, baking soda, and salt. Stir with a spoon until well combined.
Next, mix the sugar and wet ingredients. In a large mixing bowl, add the sugar, oil, and eggs, and whisk until fully combined. Next, whisk in the grapefruit juice, grapefruit zest and vanilla extract. Whisk again until fully combined. Finally, add the greek yogurt and whisk until it is fully incorporated.
Finally, mix the dry ingredients into the wet ingredients. Add the first half of the flour mixture to the wet ingredients and whisk gently until almost fully combined. Whisk in the second half of the flour and whisk until just fully combined, but be careful not to overmix.
Pour the batter into the prepared pan and bake at 350° F (180° C) for 50-60 minutes, or until a toothpick inserted into the top of the cake comes out dry. Allow the cake to cool for about an hour before glazing.