The Karate Kid - The Chain Belt Dojo has the same motto and creed "Strike First, Strike Hard, No Mercy" as the Cobra Kai in the 1984 movie The Karate Kid and Francis uses the same teachings as Cobra Kai.
The gi that the students of the Chain Belt Dojo wear is similar to the Cobra Kai.
Teenage Mutant Ninja Turtles - Francis building a dojo and teaching karate to troubled kids and using them for his operations is similar to the 1990 Teenage Mutant Ninja Turtles movie where Shredder recruits troubled children and orphaned kids in teaching them Ninjutsu to do his biddings.
Gravito suggesting for Francis to open a small martial arts school where he teaches karate to earn a living and try to make it successful in many years is similar to the very first issue of the original Teenage Mutant Ninja Turtles comic by Mirage Studios, where Hamato Yoshi formed a small martial arts school in New York after killing one of the member of the Foot when Splinter is telling the origin of how the turtles came to be.
Mary knocking Francis out with a cricket bat is similar to Casey Jones throwing Raphael into a trash can with a cricket bat during their fight in the 1990 Teenage Mutant Ninja Turtles movie, with Francis paraphrasing Raph's line about cricket before Mary hits him. Gravitress then steals the Memory Eraser Taser 200 from him to erase his memory of the fight with her husband.