Bring water a boil in a large soup pot over high heat. Add cow's foot, onion quarters, garlic, thyme, marjoram, peppercorns, and bay leaves. Boil, skimming off the foam the forms on the surface, until broth flavors intensify, about 30 minutes. Add beef tripe and bring to a boil. Reduce heat to medium, cover, and cook until cow's foot softens, about 1 hour.
Remove cow's foot pieces from the broth and transfer to a dish. Skim fat from the surface of the broth. Add hominy; cook until tripe is softened, 30 to 45 minutes. Do not overcook.
Separate meat from the cow's foot. Discard bones.
Discard onion quarters, garlic, thyme, marjoram, peppercorns, and bay leaves from the broth. Stir in meat and season with salt. Cook until flavors blend, about 5 minutes more. Pour into bowls and garnish each serving with lime wedges, finely chopped onion, cilantro, and oregano.