I can't take grey goo seriously as a threat. We deal with brown goo - that is, biological reproducers - constantly. And our biggest problem with fighting off brown goo isn't that we can't destroy it, but that it shares so much in common with us that we can't destroy it without destroying ourselves as well. We have to use highly specialized weaponry to fight brown goo.
Gray goo, on the other hand, is going to have sufficient differences from us that we can use less discriminating weaponry - EMPs, for example, which are largely harmless to us.
EMPs, for example, which are largely harmless to us.
They are harmless to our biological body, but not to the modern technology we've come to all but depend on -- being able to stop nanobots from devouring the planet but needing to destroy the Internet and mains power grid in the process would still be bad news, though one from which humans might eventually recover.
Article on space.com