If you purchased grey market you have no factory warranty whether the card is there or not. Normally grey market dealers have their own warranty which matches the factory one. If you have a valid factory warranty it ain't grey market.

You just need to be careful because if you buy a watch with an unusual or in house mvmt and you need service the grey market repair outfit will never be able to get the parts or at least the original parts, maybe chinese knockoffs. Also, the quality of some grey market repair outfits can be a big issue.