[Canonman]

This issue is only affecting the galley grey and not the bathroom grey?
When the pump is on, does it shut off when the faucet is off?
When using city water, can you hear any water running with the faucet off?
Can you estimate how much water is involved in say an hour or days time?
I doubt there is a frozen fresh water line since there is no evidence of a leak under the kitchen sink.
I'd start (you probably already did) by looking closely under the kitchen sink for any overflow or other hose connection between the fresh water supply line and the drain.
Sounds like more of an installation error than something broken.
If nothing obvious pops up, a mobile repair service might be the answer where you aren't able to take the trailer to the dealer. Most of these guys will work the manufacturer's warranty.
Good luck and keep us posted