Yes, you can. When you set the Mass File Download Related Files on the Lightning Record Page, you can provide the related object's child-relationship names to see only the files of the provided objects.

Steps to add Related Objects:

  1. Goto: A lightning record page, select the Mass File Download Related Files component.
  1. Drop it at the appropriate place. 
  1. Click on the component. 
  1. On the right side panel, you will see the Child Relationships input box 
  1. Enter the child relationship names separated by a comma.
  1. Tick the box that says "Show Only Objects having Related Files" (recommended).
  1.  Click the "Save" button -> Click "Activate" if not activated.

NOTE: If you enter the wrong child relationship name, then, by default, all related objects will be shown.