You can’t DELETE a product that Murphy’s has in Web Services.
If you do not want a product to be visible to the public you need to change it’s visibility.
- Go into the Publish section of the product page
- Change the Published status to Private by clicking on the Edit link next to the Visibility status
- Update the page
Because your website is synced regularly with Murphy’s any Murphy’s products that you delete are added back during the sync process.