Do you have any dry erase markers? I don't know about on coins, they will take sharpie marks off of the dry erase boards. If the coin was closer to uncirculated, I'd say leave it on there. Just my 2cents.
that's another thing, if the rest of the coin has toned since the marks, removing the marks will leave brighter or discolored spots compared to the rest of the surface. kind of looks like a china marker marks to me, which is why I questioned if it was sharpie. China marker is sort of an oil/grease/wax based crayon pencil, that you peel. it would be moisture resistant, even to a lot of solvents and degreasers. it might smudge a bit if wiped hard, but won't really come off without a lot of work and something that will break down the grease/wax of the china marker. if it's china marker, the only way to really remove it from metal or anything else completely is either acetone and elbow grease rubbing, WD40 and rubbing, or a baking soda and water mix and rubbing. Again though, it's fine to use it to remove china marker on a piece of sheet metal, not so much for removing it from a coin that you get rub lines on. Honestly I'd just leave it alone at this point, you tried the least harmful methods and got nowhere, there's no guarantee underneath it won't have toned at a different rate and will still have lines on the coin, i'd just leave it as it is at this point unless you decide to possibly sacrifice the coin as an exercise in learning.
Seeing several line marks and also several spots of it on the lower parts, I would suspect copper sulfide formation if none of the above trials didn't work on it. Copper Cents were extremely susceptible to acids being used to 'lighten it". The ugly bright yellow color if the person was not very careful would also be unacceptable , so they would use Dellner's darkener to darken it a tiny bit to try to make it look like a Red or Red brown cent. Dellners uses sulfur to change it. Today it seems to be gone and a similar composition is called "Brimstone Darkener", for use on copper to age it for antique appearance. I would save it like it is, Jim
Or, send it in to one of the grading companies that do restoration and see what they can do. More costly, yes, but at least you know it would be done to a higher standard. JMHO.
Goo gone did nothing but possible brighten the patina a bit. I'm going to leave the coin alone. Thanks for the suggestions.