Those shopping cart and checkout links are part of the stock Zen Cart header nav, not connected with the cart summary. You have styled the rest of the header nav links at the top of the page, but these are left over. Your best bet would be to move the cart/checkout links and their containing <li> and controlling code from tpl_header.php to the cart summary file, inside the #navMainCartSummary div (and with a new <ul> </ul> wrapper so the <li> are properly formatted).