Preheat the oven to 350 degrees . Grease and flour a 5-by-9-inch loaf pan; line the bottom with parchment paper. In a medium bowl, whisk together the eggs, poppy seeds, grapefruit peel and vanilla. In a small bowl, whisk together 1/3 cup granulated sugar and 1/4 cup grapefruit juice until the sugar is dissolved.
Using an electric mixer, beat the butter on medium speed until creamy, 30 seconds. Gradually beat in the remaining 1 1/3 cups granulated sugar and the salt on high speed, scraping down the sides, until light and fluffy, 3 to 5 minutes. Beat in the egg mixture, 2 tablespoons at a time. Scrape down the sides; mix for 3 minutes. Mix in the flour in 3 parts on low speed. Scrape into the prepared pan.
Bake until a toothpick inserted into the center comes out clean, 60 to 70 minutes. Transfer the pan to a rack placed on a sheet of parchment paper. Using a skewer, poke holes into the loaf; brush with half of the grapefruit syrup. Let cool for 10 minutes. Run a knife around the sides to loosen, then invert onto the rack and brush with the remaining grapefruit syrup. Turn right side up and let cool completely, about 1 hour.
Whisk together the confectioners sugar and the remaining 1/4 cup grapefruit juice. Drizzle over the cake and let set before slicing.