New to cast iron

I got my first cast iron skillet about a month ago and everything was all good and fine until I cooked chicken in it. The chicken didn’t burn but there was burn marks on the cast iron. As much as I scrubbed (and eventually with bad keepers friend) the black burn marks would not go away. Yesterday I got a two sided griddle and use the flat top to make quesadillas, the cheese that spilled out burned on the cast iron and the same thing happened with the black marks. Both times I used oil and both times I cleaned the pan as soon as it was cool enough to touch, is there anyway to get rid of the black marks? I know they don’t really hinder the pan but it doesn’t look nice and uniformly black/shiny anymore 😭