You can use the device Notification Control in the settings to manage which alerts you choose to receive. Simply go to your Device's settings, Notification Center (or Notifications), and tap on the Dictionary.com icon. There you will see the available options for notifications from the app.
If you are receiving two notifications, then it is possible that you have two versions installed: the free version and the Premium version. You will be able to see them both in your Notification center.