Yes. Payments are processed by Stripe, our payment processor and the merchant of record for your purchase — we never see or store your full card details.
What we keep is a receipt of your order: the order number, addresses, tracking, and a payment summary (card brand, last four digits, billing address), so you have a record of what was sent.
Your data is stored in the US and encrypted in transit and at rest — including your letter contents and saved addresses. We never sell your data.