Try this. You only delete the file if is it has been successfully sent.
$numFiles = count(array_filter($_FILES['priloha']['name']));
for ($i = 0; $i < $numFiles; ++$i) {
$target_path = './' . basename($_FILES['priloha']['name'][$i]);
if(move_uploaded_file($_FILES['priloha']['tmp_name'][$i], $target_path))
{
echo "Soubor ".basename($_FILES['priloha']['name'][$i])." byl úspěšně nahrán.<br />";
}
if ($mail->AddAttachment($target_path) )
{
unlink("$target_path");
}
}