When customers sign up for a free trial, when is the credit card verified?

Credit cards are verified at the time of signing up for the trial even though the card isn't billed. This can be demonstrated by attempting to purchase the trial using fake or invalid credit card information. Even though the card is verified it's still possible that when the card is billed there are insufficient funds.

High failed payment rates are a standard component of running a subscription business. That's why we have automated overdue payment handling built into MemberMouse: Automated Overdue Payment Handling

Please note that MemberMouse itself doesn't perform the verification on credit cards. We simply pass the credit card data to the payment processor and wait to receive a success or error response based on the internal verification they're doing. Different processors allow for varying levels of configuration of the verification settings so if additional information around verification is desired it's best to speak directly with the payment processor's support.