How to add GET variable after script url?

Filter script_loader_src and use add_query_arg(). You can use parse_url() or the second argument $handle to target specific scripts…

I have included multiple redundant options here:

add_filter( 'script_loader_src', 'wpse_99842_add_get_var_to_url', 10, 2 );

function wpse_99842_add_get_var_to_url( $url, $handle )
{
    if ( 'my_handle' !== $handle )
        return $url;

    if ( empty ( $_GET['myvar'] ) )
        return $url;

    $parts = parse_url( $url );

    // specific host
    if ( 'example.com' !== $parts['host'] )
        return $url;

    // specific path
    if ( '/foo/bar' !== $parts['path'] )
        return $url;

    // or specific start of path
    if ( 0 !== strpos( $parts['path'], '/foo/' ) )
        return $url;

    return add_query_arg( 'myVar', $_GET['myvar'], $url );
}