That is an interesting one. Generally when you have enabled Cash on Delivery as a payment method on your store, customers would simply be able to pick this as a payment option for the total amount in the checkout, and so it wouldn’t necessarily add any extra costs. A customer using a manual payment method sees the name of the payment method and the instructions to complete the payment on the order confirmation screen.
The shipping rates that you have setup on your store would be added to the total cost however - could this be the extra charge you are referring to?
Can you explain how you have implemented the COD payment method? Have you added it as a Manual Payment Method as explained in our Help Doc here, or are you using some sort of external/third party gateway integration? Also, if you are comfortable to share any screenshots of the setup it would be beneficial to get a better idea of what is happening.