Adaptation Displacement: Of a sort; the term "Gremlins" has become largely associated with the big-eared, reptilian humanoids of these films in the popular culture despite the origins being Older Than They Think and going back to World War II. However, they continue the Chaotic Evil trouble-making misschief of the older versions of Gremlins seen in Looney Tunes cartoons, so it might be more of an Evolving Trope.
Iron Woobie: Gizmo in both films, being abused by his spawned offspring, taken from Billy and Mr. Wing dying in the second film. And then the mad scientist cages Gizmo to start the whole mess all over again. Despite all this, Gizmo remains a cute, cuddly, friendly little critter, with genuine affection for most of the people he meets, but especially Billy and Kate. And in Gremlins 2, after being pushed too far, he Takes a Level in Badass.
Chaotic Evil trouble-making misschief of the older versions of Gremlins seen in Looney Tunes cartoons, so it might be more of an Evolving Trope.