jetpack-admin-menu-tweaker.php

<?php

add_action( 'admin_menu', 'nuke_jetpack_lowlevel_menu', 900 );
function nuke_jetpack_lowlevel_menu() {
	// If Jetpack isn't active, do nothing.
	if ( ! class_exists( 'Jetpack' ) ) {
		return;
	}
	// If the user is an author or above, do nothing.
	if ( current_user_can( 'publish_posts' ) ) {
		return;
	}
	// Otherwise, remove the bit of code that adds the menu.
	remove_action( 'admin_menu', array( Jetpack::init(), 'admin_menu' ) );

	// And that which might later
	remove_action( 'admin_menu', array( Jetpack_Admin::init(), 'admin_menu' ) );
}