When Gumball and Darwin realize Grandpa Louie has no friends, they create one called Muriel, when Granny Jojo finds out Louie has been spending time online with another woman, Muriel not existing isn't going to stop her from being destroyed. 
On the walls of the pet store is the motivational poster of a groundhog lifting a weight that Gumball showed to Mr. Robinson in "The Poltergeist." The photograph displayed below it is a modified version of one of the cat pictures featured in "The Internet."
The title of the episode may be a reference to the MTV TV Show "Catfish".
The show is presumed to have created the term Catfish, as referring to someone who pretends to be someone they are not via the internet.
The pictures of Gumball that momentarily show when Gumball is remembering things he has seen from looking up his name is a direct reference to fan-art that can be seen throughout multiple social media sites, including DeviantArt.
The line "four score and seven years ago" is a reference to the text of "Gettysburg Address" used in Lincoln's speech, referring to when the Declaration of Independence was signed.
The scene where Granny Jojo is covered in flowers is a reference to American Beauty.
When Louie describes his current view on Granny Jojo, Mussorgsky's Night on Bald Mountain is heard in the background.
The painting that Gumball mistakenly creates while trying to paint Banana Joe is a reference to the American artist, Jackson Pollock.
When Louie is sending messages via mobile, it relates to many teenagers sending small portions of a sentence in chats.
When Louie says "is so clear" a part on one of his arms are colored white.
Rocky's demonic profile picture from "The Slide" appears on his Elmore Plus page in certain angles.
When Louie on ElmorePlus chat says "Tell me more about you" Gumball is using his own account when he should be using the fake Muriel account, Otherwise Louie should've known it was Gumball.
Louie's story started four scores and seven years ago. A score is equivalent to 20 years, thus his story started 87 years, but he stated in "The Signature" that he was 72 years old.
His message reads, "...four scores and seven years ago,..." but Gumball read "...four score and seven years ago..."