It's your quotes. Use single quotes and change the if statement to '$0.00 USD'
instead of using double quotes.
<tbody>
{foreach key=num item=referral from=$referrals}
{if $referral.commission != '$0.00 USD'}
<tr>
<td>{$referral.date}</td>
<td>{$referral.service}</td>
<td>{$referral.amountdesc}</td>
<td>{$referral.commission}</td>
<td>{$referral.status}</td>
</tr>
{/if}
{foreachelse}
<tr>
<td colspan="6">{$LANG.norecordsfound}</td>
</tr>
{/foreach}
</tbody>