Let me tell you that grout pens only work effectively on clean surfaces... It is required to have a clean (not dirt and free from grease) and dry surface. Grout pens only work for discolored surfaces. I don't recommend Grout pens if your surface is dirty...
I think you should use sand paper because it works more effectively, however this will take you the whole weekend depending on how big your tile surface is.
Good luck and let us know if you get it off.