Welcome to the Community, @lbandy. I'm here to answer all your questions about QuickBooks Payments.
For customers paying an emailed invoice with the payment link, there will be a pop-up message from the merchant saying "declined-invalid transaction."
For credit card payments entered manually as a phone payment or card swipe, you will immediately be prompted that the card is declined. In this case, you'll need to contact the cardholder to re-process the card.
For future reference, read through these articles to learn more about QuickBooks Payments :
Get back to me if you have any other concerns. I'd be delighted to help you.