Cómo cambiar oculto en HTML
$('#check').change(function() {
$("#delete").prop("hidden", !this.checked);
})
Awful Anteater
$('#check').change(function() {
$("#delete").prop("hidden", !this.checked);
})<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.11.1/jquery.min.js"></script>
<table>
<tr>
<td>
<input id="check" type="checkbox" name="del_attachment_id[]" value="<?php echo $attachment['link'];?>">
</td>
<td id="delete" hidden="true">
the file will be deleted from the newsletter
</td>
</tr>
</table>