If you are not responding the letters seem to come on a 2 to 3 months interval. If you do respond a reply will usually come as soon as your letter is read or about two weeks after you mail it.
If it were me I would send them one letter letting them know that there is no such image on your site and that Pic-Scout picked up an image that was hotlinked, cite the perfect 10 v. Google case that ruled linking is not infringement and let them know you consider the case closed and will no longer respond to any letters. You may also want to add if they choose to continue sending you letters you will file complaints with the Washington state Attorney General's office, the Better Business Bureau and the Federal Trade Commission.
If it were me I would send them one letter letting them know that there is no such image on your site and that Pic-Scout picked up an image that was hotlinked, cite the perfect 10 v. Google case that ruled linking is not infringement and let them know you consider the case closed and will no longer respond to any letters. You may also want to add if they choose to continue sending you letters you will file complaints with the Washington state Attorney General's office, the Better Business Bureau and the Federal Trade Commission.