If a product is discontinued (and you will not be restocking it) then you don't have to do anything.
You can leave the product in your Back In Stock - Restock Alerts app account. Since it's no longer available to purchase the customer notifications will not be sent.
If you would like to remove the product from your Back In Stock - Restock Alerts dashboard (for example, you don't want to see it in your reports anymore) it can be deleted using the Products report:
Visit the Products link on you app dashboard.
Select the discontinued products by click the checkbox next to each one
Click the red Delete button at the bottom of the report.
This will delete the product and the customer notifications attached to it.
Note: You should be sure you won't be restocking a product before you do this.
Not able to remove a discontinued product from the dashboard? Please reach out to us for support.