I would like to assure you that your payment details are kept on a secure server and are not shared with any third parties. Access to this data is extremely limited. Moreover no one can see your whole credit card number.
Anyway in order to edit or remove your credit card details just follow these simple steps:
1. Click on the Pencil button here -> http://screencast.com/t/6nqXAeiK4a
2. Click on the red cross;
3. Click on the Pencil button again to confirm your actions.
Let us know if there is something else we can help you with.
Hi Bango, if you clicked the link in Alonya's reply it only takes you to a screenshot of an example of what it looks like, the drachmas in the screenshot are just an example, they are not your actual purchase. You would need to get back to your main game page and click "bank" and click on something to purchase then click the saved card which has a green tick or check mark on it then you should see something similar to what is in the link's screenshot. if you click the pale grey pencil in the top left that will allow you to edit your card preferences. A red X should then come up. Click that, make sure your card details are no longer displayed, then don't forget to click the grey pencil again which will save your changes. Your card details should now be removed.