When you open the related table chart widget in Web App Builder, at the top of the widget is the option to search by address, similar to the Search widget.
I'm currently using the related table chart widget to show stocking information for lakes. The search bar in the widget does not recognize the names of the lakes that I am searching for, making it useless for this application. So what I would propose is one of two options: 1) have an option to hide the search bar; or 2) Allow us to set the service that the search can draw from, similar to how the Search widget can be configured (this would be my preference).