If you want more goose genetics, I think I learned it from here:
https://www.backyardchickens.com/threads/our-guide-to-colour-and-pattern-genetics-in-geese.561779/
I have not done it, but I have read about the genes involved.
The dilution gene is on the Z sex chromosome.
A goose has ZW, so a Pilgrim goose has one copy of the dilution gene, and she passes that only to her sons.
A gander has ZZ, so a Pilgrim gander has two copies of the dilution gene...