I’m sorry, I don’t use BuddyPress so I’m not sure how much help I can be.
I know what the “BuddyPresss Members Directory Page” is, that’s the ‘/members/’ page, yes?
But as for “the ‘Clear’ button that resets the page to the unfiltered view of the Members directory”, I don’t know what that is. I’ve looked at the ‘/members/’ page using a default WordPress theme and I don’t see a ‘Clear’ button so perhaps this is related to an additional plugin you have installed and activated?