My thoughts on this topic:

1) Limited reparenting is an intrinsic part of any long-term relational psychotherapy (person-centered, psychonalytic, ect). This involves teaching stuff in the relationship via experience - emotion recognitition, emotional regulation, trust, setting boundaries, self-reflection etc etc. Essentially all the things that parents teach their children via just having a parent-child relationship with them without perhaps ever explicitly talking about this teaching taking place. These same things also happen in every long-term relational therapy (and don't get started about psychoanalysis - I don't believe that you will find an unrelational analyst knowadays), without just calling it a fancy name.

2) So where does the fancy name come from? I would guess that from schema therapy. Schema therapy is one of the so called third wave cognitive therapies (the first wabe being the biheivioral therapy, the second wave is the CBT), which expands the standard CBT with "new" principles and methods which are essentially just things that other therapist (person-centered, psychoanalysts, gestalt therapists) have known and adopted for decades. My guess is that these approaches are given fancy names because they contrast to the standard CBT where the therapeutic relationship is assumed but otherwise not paid much attention to (i.e if the patient is not able to form a productive therapeutic relationship to do the cognitive work then the patient is simply not ready for therapy).

That opinion is of course a bit too unfair regarding to some cognitive therapists who, aside for working with cognitive restructuring and all the related techniques, quite naturally also adopt all this relationship business in their work, without perhaps even realising that what they are doing is not so much different from what a person-centered therapist or a psychoanalyst is doing.

3) But yeah, I agree what one of the posters said - what some therapies call reparenting or limited reparenting, is in fact the core therapy work of long-term relational therapies and has been like this for decades, just without a fancy name. All the skill-based stuff is of course nice, but I personally wouldn't call it a psychotherapy. Sure, it can be some kind of therapy, such as there are physiotherapy, speech therapy etc. So it could be psychological skill therapy or something like that. But to my mind real psychotherapy is something that aims to reach deeply into the persons psyche in order to help to learn new ways of relating to self and others and to my mind the only effective way for doing that is via the experience embedded in the relationship.