Refund through Stripe (or however you were paid), then record it on the booking.
Pillowcase never moves money on your behalf, so refunds are issued by you: through your Stripe dashboard for card payments, or however the guest originally paid.
Once you've refunded, open the booking and mark the refund as issued. That records a refund transaction against the booking, so your transactions page tells the full story.
A cancelled guest will usually expect money back on the card they paid with, so it's worth issuing refunds promptly after cancelling.
Email support@pillowcase.io with your campsite name or booking reference and we'll pick it up from there.