Rinse the tripe and calves’ feet, if using, in several changes of cold water.
In a bowl large enough to hold the tripe and calves’ feet, combine the vinegar, 4 cups of water, and 1 tablespoon of salt, stir to dissolve the salt. Add the tripe, calves’ feet, and enough additional water to cover and soak for 30 minutes. Drain in a colander and rinse well.
Cut the tripe into bite-size pieces, 1 to 1 1/2 inches.
Add 5 quarts of water and the onion and garlic in a very large soup pot or a stockpot. If using the calves’ feet, add them to the pot and bring the water to a boil over high heat. Reduce the heat to medium and simmer, partially covered, for 20 minutes. Skim off any foam.
Add the tripe to the pot, along with the remaining 1 teaspoon salt, the oregano, and mint-sprig bundle, and bring to a boil. Reduce the heat to low and simmer, partially covered, for 4 hours, or until the tripe is soft and tender but still has some texture. Remove the garlic and onion and discard.