MK II frag grenades were painted OD (MS 34087) throughout WWII, indeed the current baseball grenades are painted the same color today.

The yellow band where the fuze screws in indicateds the type of fuze. Initially to denoted the difference between a MK I and MK II grenade, the only difference between the two being the inproved M64A1 fuze. The two thin bands indicate an M64A1 or M201 fuze, one thicker band being used to show an M10A3 fuze.

The spoons are not painted. They are plated with a very thin zinc galvinizing formula. It has a green dye in it to give the tint you see on most of them. The lower inch of the spoon is dipped in very thin black laquer, purpose unknown. The model and lot number of the fuze assembly are painted in black on the flat that covers the striker assembly.

Photo of original grenade spoons collected from WWII Training Camps used from 1942-1944, courtesy of Mike (via email)
As you will see, some were painted and some were zinc galvanized

If the spoon is rusted and must be refinished, I guess I would paint it MS34087, the same as the rest of the grenade. If it still has that unpainted greenish hue I would leave it alone as that is the original plating. If it is the blue spoon that comes on the current copies, I would throw it out and get a correct one. The one on a smoke grenade will work once the angular bends are removed.