Removing Add New button from table home page

Hi!

I have this exact setup in my app and it works great ... sometimes.

I'm running into issues with dropdown lists - for example:
Three tables - Customers, Work Orders, Products
- User is viewing a customer record.
- User clicks the "Create a new work order request" button which creates the related child record.
In the New Work Order form, there is a dropdown list where the user needs to select the (related) product for the work order. In that related products list, they don't have the ability to add a new product if it isn't already listed in the product table. 
Is there a way around this?

The column on the User Interface screen says "Hide Add Button/Links" which is disappointing. Is there a way to hide the button yet allow the user to create a related child record from the dropdown list?