it is perfectly safe to use stainless steel wool on a Vitreous enamel. I presume that the cast iron skillet has a Vitreous enamel finish.
The reason is simple:
Vitreous enamel is essentially a type of ceramic and has a hardness of around 5-6 on the Mohs scale. Steel has around 4-5 on the same scale. This means that generally, you can not damage it with the steel wool.
Also no not confuse the "grit" of the steel wool with its hardness :P
The only thing that will happen is that the enamel will get very small scratches and that things will stick a bit better in them. You can get rid of most of them with a good polishing compound if they disturb you to much.
Personally I would advise you "not to need" to clean it with steel wool in the first place, but is something burned up badly and you do not have heavy cleaning agents nearby steel wool is an acceptable solution.
If it is just for cleaning leftovers , usually soaking in soap water and a hard plastic brush does a very good job as well.
Remember that even thou Vitreous enamel is very hard and durable it may be damaged by overheating or crack if dropped.
This is quite common and pretty harmless. The scratches you see don't go very deep, nor are they very wide. My All-Clad saute pan is nearing 10 years old and has a ton of micro-scratches on the interior. It still performs beautifully.
That said, the scratches can grab onto proteins and cause sticking. However, this is simple to prevent with both oil and proper pan preheating.
When a pan is preheated properly the metal expands, essentially closing all of the micro-scratches. This prevents the proteins from grabbing onto them and getting stuck. You obviously need oil/fat to assist with this as well.
To properly heat a pan to the appropriate temperature I suggest using the water drop method. If you put a cold pan on heat and drip a drop of water onto it, the water will sit there for several seconds then boil away. As the pan gets warmer this will happen more quickly, fizzling away in a second or so. Once the scratches start to close something weird happens.
First, the drop of water will break into a few mini drops which scoot around the pan as they evaporate. This is a sign that you are almost there. When the drop of water stays whole (mostly) and scoots around the pan like a mercury ball, this is the perfect temperature. I the water instantly vaporizes on contact, you've gone way too far and need to let the pan cool down. At this point you should add your oil/fat, swirl it around, and immediately add your food. (Make sure the mercury ball of water is gone before adding oil).
Also note that the mercury-ball phase is definitely too hot for unclarified butter, and may be too hot for some extra-virgin olive oils. They may instantly smoke upon adding.
Again, it's important to have your oil and ingredients in place (mise en place) before you start. It's quite easy to skyrocket past the mercury-ball phase if you have to open your oil, pour, and then season your ingredients.
Best Answer
Can you smell bleach?
If yes, rinse it & use it.
If not, just use it.
Is it stained?
If not, just use it.
If yes, you can remove the staining with bicarbonate paste made with water or Barkeeper's Friend.
Once any staining is gone, the natural coating [chromium oxide passive layer] will reform.
Just cook with it as normal.