"The Family Guy" is a common misnomer given to the show, properly known as "Family Guy", in both real life, and in the show, itself. The concept of uneducated outsiders addressing the show by this title has been joked about and referenced to a number of times in the series, mostly via fourth wall jokes.
While in Italy, The Griffins fill out an application to go back to America. When the agent reads their papers, he notices that for "Occupation", some of them wrote "Family Guy" and some of them wrote "The Family Guy" and asks which is the true title. Annoyed, Peter looks back at his family and scowls before turning back and telling him the correct title of the show.
Lois erroneously refers to Star Wars as "The Star Wars". Slightly peeved, Peter corrects her. This is similar to how people who don't watch Family Guy or aren't very acquainted with the show, will often call it "The Family Guy" instead of just "Family Guy".
In the museum of television, A couple of tourists walk by Peter, while he pretends to be a statue. When the female tourist asks her boyfriend, who that is, her boyfriend scoffs and says "It's that fat idiot from The Family Guy." They both say that they hate the show and walk off, leaving Peter crying.