SnagRes stores the minimum needed to send you reservation alerts: your email address, which restaurants you have starred, and your alert settings. Sign-in runs through Google OAuth, so SnagRes never sees or stores a password.
SnagRes does not store payment card details. Subscriptions are processed by Stripe, which holds that information under its own terms.
You can delete your account and everything attached to it from the account page at any time, which removes your email, your starred restaurants and your alert history.