You should know that Nikon and other camera companies will not even let you pay them to repair grey market items. You're basically SOL of something goes wrong.
That may not be true, and the distinction should be made regarding Nikon USA service, Nikon service facilities outside the USA, and other camera makers policies.
Some US sellers of gray market Nikon gear, like
B&H Photo Video, have you send a Nikon to them during the warranty period and
B&H handles getting the camera repaired under warranty.
U.S. Grey Market Products B H Photo Video
Nikon USA Service will not work on Nikon gear, even for pay, that does not have a US serial number.