BuddyPress.org

function bpfr_remove_change_avatar_tab() {
global $bp;
	bp_core_remove_subnav_item( 'profile', 'change-avatar' );

}
add_action( 'bp_ready', 'bpfr_remove_change_avatar_tab', 15 );

BuddyBar items

Source: bp-core-buddybar.php
function bp_core_remove_subnav_item( $parent_id, $slug )
and to remove a nav item
function bp_core_remove_nav_item( $parent_id )