You can unsubscribe from any emails that have an unsubscribe link at the bottom of the email. If you can’t find that link in the email, you won’t be able to unsubscribe from that type of notification because they keep you up to date on your account activity.
There are some emails and push notifications that you can customize. If you go to the Notification settings of the Settings page on your Petal dashboard, you’ll be able to customize the push notifications and emails that are listed in that tab.