GHK selectively transports copper to the tissues it's needed, it remains bound to "excess copper". That being said, high dose injections can cause tissue damage locally.
Can't post studies here unfortunately. Google the research using biotinylated GHK on rat wounds showed a ninefold increase in copper concentration at the site of injury.
It's going to blow your mind when you find the research demonstrating very high elevations of copper in metabolically active tissues, and not other tissues. I'm sure you'll say that's a mechanism and not an outcome, but it indicates tissue selectivity.
Excerpt from another paper:
Many researchers proposed that, at the physiological pH, GHK-Cu complexes can form binary and ternary structures which may involve amino acid histidine and/or the copper binding region of the albumin molecule. Lau and Sarkar found also that GHK can easily obtain copper 2+ bound to other molecules such as the high affinity copper transport site on plasma albumin (albumin binding constant log10 = 16.2 versus GHK binding constant 16 log10 = 16.44). It has been established that copper (II) redox activity is silenced when copper ions are complexed with the GHK tripeptide, which allows the delivery of nontoxic copper into the cell [12–14].
Bioavailable copper is what dictates homeostasis. You have to be exposed to excess bioavailable copper for homeostasis to be affected. If free copper is high, you're in trouble. This is why it's reallllllly ill-advised to arbitrarily use copper supplements or zinc supplements without concern for dosing and ratios.