If I mark an order as Refunded, does the money go back to the customer's card?

No. Changing the status to Refunded records the refund in Wcart. It doesn't move any money through your payment gateway.

To return the money, issue the refund in your payment provider's dashboard (Stripe, Razorpay and so on), or pay it back by bank transfer or cash.

When an order is marked Refunded, Wcart does reverse its credits: wallet money used goes back to the customer's wallet, reward points are adjusted, the coupon is freed and affiliate commission is reversed if unpaid. The order's total also counts in the Returns tile on the Orders page.