If you are in the Free Edition product and have not added the PLUS benefits, you should not have to submit a credit card number to file an extension.
Here is a FAQ on how to file an extension for reference.
https://ttlc.intuit.com/replies/3301811
Hi - yes, filing an extension is free, but you still need to file your return at some point, and so you are likely seeing a payment for TurboTax for that reason. Hope this helps.