I’m not sure how this myth even got started. How if you or your pet gets sprayed by a skunk to use tomato juice in a bath to get rid of the mell. It does not work. If anything it will make it smell even worse!
The thing to do if you are so unlucky to be sprayed by a skunk is a home remedy that has 1 quart of 3% hydrogen peroxide, ¼ cup baking soda and 1 teaspoon liquid soap. The soap breaks up the oils in the skunk spray and allows the other ingredients to do their work to get the stank out. At the end you should rinse it all off with water. Being careful to not get it in the eyes.
But absolutely no tomato juice.