Permanent marker is fine on a laminated chart. The CAA charts don't last too long anyway because they're always updating them, but if you erase the lines by scribbling over them with a whiteboard (non permanent) marker, then wipe with a tissue, it doesn't wreck the chart.
Cleaning it with solvents, as I've seen some people do, is a different story.
I appreciate the debate about how often to look at the chart, but I wrote what I've been taught and it works for me. I also find it easier when an ATSU suddenly asks me my positon - I know where I am now, not where I was six minutes ago or where I think I should be.
The original poster should do as his Instructor says with chart reference, that's what the Instructor will want to see and that's what he's paying a lot of money to be taught.