I'm not sure if I understand what you’re asking,

Are you saying that users may enter invalid card  details? Or

Are you saying how users can trust your system?

The first one is easy,

1. Start the registration

2. Confirm the details with the bank of card issuer

3. Charge them on their account

4. Commit the transaction

5. Create an online  receipt for the user for their further query

For the second one it’s even easier,

People will not enter their credit card details just anywhere, and if they have entered their details in your system, they must have thought that your system is legitimate enough.

One more thing is that, they might have used a certain type of credit cards that banks issue for only a single transaction with a limited amount.

For instance you want to register somewhere which you are not really happy with using your regular card (the one that you usually use) so you ask the bank to give you a card that is only valid for one transaction with amount of i.e. $100. You use this for a registration somewhere. Once you used this card, you can no longer use it again as it was for a single-use purpose. So the user is guaranteed that they are not going to be charged on that card twice.