Cast Iron care is a simple source for many arguements and disagreements.
Many methods are listed here and some methods disagree.
It sounds like you have simple moderate surface rust. Yes electrolysis will remove it, however that method will remove ALL of the seasoning on the cast iron piece---and it sounds like you do not need to get that drastic. Soaking in lye will remove all seasoning and rust, but also is a drastic measure.
Some folks say use soap and water or SOS pads with soap in them. Others pull their hair out at the mention of soap and cast iron in the same sentence. Soap can be used on well seasoned cast iron, because the seasoning's coating protects the porous cast iron from soap residue leaching into the pores. If you have "rusty" cast iron then it is not "well seasoned" and therefore may soak soap smell and taste into the cast iron.
Some folks say use a wire wheel on a rotating drill to remove the rust. Rotating wire wheels work great on cast iron that has never been seasoned---but seasoning is mainly carbon and wire wheels rotating fast seem to "swirl" the seasoning that exists in cast iron that has been previously seasoned.
In getting rid of rust---the cast iron should be inspected to see if it has ever been seasoned and then decide---either remove all rust and all seasoning ---or remove surface rust and do minimal damage to the existing seasoning.
Acidic liquid will remove rust and also remove seasoning---but acid removes it at a slow, controlable pace----so cast iron can be soaked in acidic, vinegar, coca cola, citric juices, etc. and lightly scrubbed with scrubbing toolsuntil the surface rust is gone and the piece requires rinsing and then a light coating of seasoning---rather than completely removing everything and starting over with seasoning process.
I cook, cater and do historical reenactments using cast iron equipment and have restored many pieces of cast iron---but I am not an expert. I have found that 20 people will give you 20 different opinions. I have stumbled along and try to do as little damage to a piece of cast iron while simply trying to make it usable.
I vote for soaking in vinegar then light scrubbing with a stainless steel, brass, or best of all plastic scrubber. (trying not to scratch up previously seasoned piece) If a utensil is needed to scrape harder try to use a wooden spoon or a bamboo utensil to avoid marring surface. Rinse cast iron then heat it up to make sure no moisture is retained in cast iron pores and lightly season with whatever you use. I use olive oil because I can get it cheap or free from local olive oil producers. I use vinegar because it is cheaper than Coca Cola or other acidic liquids, and is easy to buy by the gallon. I do not use these products because I think that they are the only thing to use----I use them because they are "easy" for me.
Happy cookin on your cast iron cookware
This is simply how I do it
