The evidence
What the research actually says
The clearest single source is a review by Pickart and Margolina, published in the International Journal of Molecular Sciences in 2018. It gathers decades of laboratory and small clinical work on GHK-Cu, describing the peptide as playing a role in skin remodeling and in the signals cells use during repair.
A review is a summary of other studies, not a single large trial. Much of the underlying work was done in cell cultures or in small groups of people.
Copper peptides are one of the more researched ingredients in this category. That does not make every marketing claim about them true.
So the honest framing is this: GHK-Cu has been studied for support of skin repair and the appearance of firmness, and the results look promising — but the strongest claims still need larger human trials. We say may help, not proven to cure.