I know some will disagree with me, but I suggest you try some good quality oil and coarse rag first and rub hard. I also use a pencil eraser for small spots. 0000 steel wool and oil will work, but be judicious in the use and only as a last resort. The action was originally case hardened, I believe (I have one in .410 that showed some slight signs of case color until I began restoration).

Jim