Dan >>> First, do you want to remove JUST the courier price from the summary section, not the dropdown select? If so, why? Unless your only courier price is zero your summary charges won't add up, which is not particularly good practice. If you do have just a zero courier price then why not hide the courier select as well?
Second, if you do want a single zero cost delivery option, then you can - set up one courier with zero price - remove the '<option value="">$lang[choose]</option>' from the tpl - hide the <tr> containing the dropdown select - hide the <tr> containing summary delivery cost - if you are not using the Tax and Discount plugin then add a bit of javascript at the end of your form to call the ordersCouriers function when the page intially loads
If you're using Tax and Discount plugin them the changes need to be done in taxAndDiscount.tpl, otherwise orders_delivery.tpl.
If you were to remove the <tr>s instead of hiding them you would break the javascript routines for Tax and Discount and Product Attributes. If you are using them now, or if there is the possibility of using them in the future, then you are better off hiding the courier stuff rather than removing it.
See also topic numbers 473 and 2070
PS. Hide means setting style='display:none;' on the tag.