Array
(
    [0] => Array
    (
        [background] => https://example.com/image.jpg
        [description] => Example text
        [url] => https://example.com
    )

    [1] => Array
    (
        [background] => https://example.com/image.jpg
        [description] => Example text
        [url] => https://example.com
    )
)

$array = append_field($array, 'url', '?parameter=test');

function append_field($array, $field, $parameter)
{
    foreach ($array as $inner_array) :
        foreach ($inner_array as $key => $append) :
            if ($key == $field) :
                $append .= $parameter;
            endif;
        endforeach;
    endforeach;

    return $array;
}