Becoming righteous is spoken of as if it were washing one's clothing. See how you translated as similar phrase in [Revelation 7:14](../07/13.md). AT: "those who have become righteous, as if they have washed their robes" (See: [[rc://en/ta/man/translate/figs-metaphor]])
In that culture the dog was an unclean, despised animal. Here the word "dogs" is derogatory and refers to people who are wicked. (See: [[rc://en/ta/man/translate/figs-metaphor]] and [[rc://en/ta/man/translate/figs-explicit]])