You could try oven cleaner.

Get the stuff that does not require heating up the oven.
Wet down the marks. then also wet down some paper towel and place it over the marks.
Place some seran wrap etc. over this mso the oven cleaner does not dry out.
Let is sit for a couple hours to see if it will soften up so you can clean it.

If you use powdered dishwasher soap you could try mixing a fairly strong solution of it in some water and then use that instead of oven cleaner.