The gray goo is predicated on the sort of thinking common in bad scifi.

Basically, in scifi the nanotech self replicators which eat everything in their path are created in one step. As opposed to realistic depiction of technological progress where the first nanotech replicators have to sit in a batch of special nutrients and be microwaved, or otherwise provided energy, while being kept perfectly sterile (to keep bacteria from eating your nanotech). Then it'd get gradually improved in great many steps and find many uses ranging from cancer cure to dishwashers, with corresponding development in goo control methods. You don't want your dishwasher goo eating your bread.

The levels of metabolic efficiency and sheer universality required for the gray goo to be able to eat everything in it's path (and that's stuff which hasn't gotten eaten naturally), require multitude of breakthroughs on top of an incredibly advanced nanotechnology and nano-manufacturing capacity within artificial environments.

How does such an advanced civilization fight the gray goo? I can't know what would be the best method, but a goo equivalent of bacteriophage is going to be a lot, lot less complicated than the goo itself (as the goo has to be able to metabolize a variety of foods efficiently).