The warranty would be honored via the seller if he is authorized, in which case you’d send the cartridge back to him, and he’d interface with Koetsu. So be sure the seller is a Koetsu dealer. This would be the first time I’ve ever heard of a Koetsu for sale on eBay from a Japanese source. So caveat emptor.
On the other hand, I bought my Urushi in Tokyo direct from a dealer, got a warranty document with it. When later I had an issue, the warranty was honored, no questions asked. If there’s a problem, the cartridge has to go back to japan regardless.