Advance Search Attributes are not removable on new custom object created

Summary:

We have created a custom object named 'Cremation Target' and by default automatically there are some fields came on Advanced Search as you can see in below screenshot. Now here i want to remove attributes "Cremation Targets Name", "Record Number" from Advance Search UI. I tried to do via Page Composer but it is not getting done as there is no option to remove these fields.

My requirement is to remove these standard attributes "Cremation Targets Name", "Record Number" (of new custom object) from Advanced Search UI. But at same time i want to keep these fields under button 'Add' so whenever user needs then they can select these fields from 'Add' and use them to search data.