In the comics, Duela Dent is also known as The Joker's Daughter. While the character has had several iterations in comic book canon, one of the best known comes from The New 52. In that version, a young Duela Dent cut her face with a box cutter and, despite being taken to the hospital by her parents, struggled against the restorative surgery, leaving her face half-deformed. Her parents were horrified by her appearance, but Duela embraced it and, ultimately, ran away from home for Gotham. After finding the Joker's face - and mistaking it for her own - Duela began wearing that face, becoming The Joker's Daughter.
In DC Comics, Duela Dent is the biological daughter of Three-Face and Jokester from Earth-3, originally using the alias Joker's Daughter. Throughout her career as a vigilante she has used the names Card Queen, Catgirl, Harlequin, Penguin' Daughter, Riddler's Daughter, and Scarecrone. She has been a member of the Teen Titans and Titans East. This version is based on the one that debuted in the New 52, where Duela is a young girl from Earth Prime who is obsessed with the Joker. She went as far as using the Joker's mutilated face as her mask.
Luke mentions Duela Dent's "Uncle Harvey", an obvious reference to Batman villain Harvey Dent/Two-Face, who is scarred on one half of his body. However, he describes Harvey as a "beloved ADA", suggesting that he hasn't become Two-Face yet.
While looking for a bright pink van on their computer tracking system, Luke also finds a pink Lamborghini roaming Gotham. This could be a nod to Joker's ride in Suicide Squad (2016).
The title, "Grinning from Ear to Ear", isn't a quote from 'Alice in Wonderland' like many of the show's titles. However, it is an idiom often used to describe the Cheshire Cat, one of the main characters in the book.