Preheat the oven to 325 degrees F (165 degrees C).

Zest 1 lime, then juice all 4 limes. Combine lime zest, juice, cream, sugar, eggs, egg yolks, and ginger in a large bowl. Whisk until well combined and pour into the prepared crust.

Bake in the preheated oven until set, about 45 minutes. Let cool slightly.

Meanwhile, heat lime marmalade over low heat until melted. Remove from heat and cool slightly, about 5 minutes. Pour lime marmalade over the warm tart and spread out evenly. Allow to cool completely before slicing and serving.