To blot out is to cover or hide, especially with ink or paint. Sometimes building owners will blot out graffiti by covering it with paint, and other times they'll attempt to scrub it off with soap.
If you misspell a word in a letter you're writing in pen to your grandma, you can start over, or you can blot out the mistake and re-write the word. Painters commonly blot out parts of paintings they're not happy with, and even tattoo artists can often blot out old designs by covering them with new ones. Experts guess that blot comes from the Old Norse blettr, "stain."