One of the ways to do it is with CSS.
You need first to find the class of the target button and then hide it with something like 
.class-button{
         display:none;
}
		
	 
	
	
	
 
		
			
	
	
		
		In your theme dir, create an over-ride of this file.
buddypress\bp-templates\bp-legacy\buddypress\members\members-loop.php
How to over-ride a BP template
Theme Compatibility & Template Files
In the over-ride, remove this code: 
<div class="action">
	<?php do_action( 'bp_directory_members_actions' ); ?>
</div>
		
	 
	
	
	
 
		
			
	
	
		
		 @shanebp that worked!  It was quick and easy since I had already made some previous changes to the members-loop.php file (which I’ve placed in a child theme folder). When I posted my question here, I wasn’t sure what to look for inside that file as I hadn’t seen any code reference to ‘button’ or ‘friend’.  So thanks a bunch for pointing me to exactly what I needed to remove!
@aymana I appreciate your suggestion too.
		
	 
	
	
	
 
		
			
	
	
		
		In the BuddyPress settings, you could just turn off the Friend component.
		
	 
	
	
	
 
		
			
	
	
		
		 @mrjarbenne that’s true, but I want the Friend functionality to be in place… just on the member profile pages, though.
		
	 
	
	
	
 
		
			
	
	
		
		Ahhh, of course. Sorry I misread.