Only custom alerts can be edited. Default alerts must be overridden in order to change their behavior - in other words you must create a custom alert that negates the default alert.
To edit a custom alert, navigate to the alerts tab/page for the entity and make your edits.
To delete a custom alert, navigate to the alerts tab/page for the entity, select the alert and click Delete.
You can turn off any type of alert without deleting it - that way you can reactivate it at any time. You can also override an alert for a specific user or set of users.
While you cannot delete default alerts, you can override them by creating a new alert that negates the instruction of the default alert.
To turn off an alert completely: