Hi Angeline,
The search results page uses exactly the same template as the members directory page, so if you modify the members directory template you actually modify both pages.
That said, the ‘All Members’ text marks one of the two tabs in the members directory. The other tab is ‘My Friends’, which is shown to logged-in users only.
So, if you wish to keep the two tabs, you can’t remove the ‘All Members’ text but you can certainly change it to something else, and possibly remove the members count. The template to modify is /wp-content/plugins/buddypress/bp-templates/bp-legacy/buddypress/members/index.php