It all depends on the composition of the dirt and how it is stuck on the card. If it were me I would do as suggested and try removing a small piece of dirt by gently rubbing with a Q tip and water and see what happens. Be gentile and good luck.
edited to add..... I have had this card for many years and have always contemplated getting the dirt on the back of it off but have just never done it. I think it would improve the appearance.
