This should be more streamlined, but here's a quick fix to exclude that single product.
Apply to modules/Recommended_Products/recommends.tpl
Code:
{section name=num loop=$recommends}
{if $recommends[num].product ne "Ebay Auction Payment"}
<LI>
<SPAN class="ItemsList">
{$recommends[num].product}</SPAN>
</LI>
{/if}
{/section}
A better way would be to create a new field, perhaps in the products table, that could be set to exclude products from the recommended list. Then in recommends.php, you could add a conditional check to determine whether or not a product should be included. Then you could manage the exclusions from the modify product/create new product pages.