They mention in the faq that they use Stripe - https://www.terminal.shop/faq. Stripe does offer integrations that are not natively using their widgets. Ultimately, the PII data is stored at Stripe.
PS: I work at Stripe but I don't really work on the PCI compliant part of the company.
PS: I work at Stripe but I don't really work on the PCI compliant part of the company.