This table is generally used for emails as a substitution.
See example below:
Edit using CSS
It is not possible to change the HTML content of the %order_items_table%. However, it is very easy to change the styling of it.
In the case of an email, you would just edit the <style> tag near the top of the email and put in the styles you'd like to use on the table (e.g. no borders, etc.). All of the elements should be marked with an ID and/or a class attribute, so you can create CSS that will target those elements specifically. (see the example HTML below)
<table id='order_items_table'><tr><th class='product-code-header'>Product Code</th><th class='description-header'>Description</th><th class='quantity-header'>Quantity</th><th class='price-header'>Price</th><th class='extended-header'>Extended</th><th class='download-header'></th></tr><tr class='order-item-row'><td class='product-code'>27373</td><td class='product-description'>CZ SCORPION PROSTOCK MAGAZINE RELEASE LEVER (BLACK)</td><td class='align-right product-quantity'>1</td><td class='align-right product-price'>$28.00</td><td class='align-right product-extended'>$28.00</td><td class='product-download'></td></tr></table>
CSS is a better solution than changing the source code… because this table is in the core, any changes to this would simply get overwritten whenever we push updates out.