Hi @guypeled,
if you are using the Live Ajax Search without the core SearchWP plugin, the search will be run using the default WordPress query_posts.
You can customise the query_posts arguments and exclude any page by ID adding the following code to your functions.php:
add_filter( 'searchwp_live_search_query_args', function( $args ) {
$args['post__not_in'] = [123,234]; // List all posts IDs that should be excluded from the search.
return $args;
} );
I hope this helps!