This is what works for me. The empty curly brackets seem superfluous, you may know a better way to code it to hide that delete box if true :
<?php if ($eCart1->ConditionalTotal("Quantity", "RecID", "" . $eCart1->DisplayInfo("ID") . "") >= 1) { } else {
?>
<input type="checkbox" value="<?php echo $eCart1->DisplayInfo("ID"); ?>" name="eCart1_Delete_<?php echo $eCart1->DisplayInfo("WAUID"); ?>" />
<?php } ?>
Thanks