In includes/languages/english/YOUR_TEMPLATE/header.php, check the value of HEADER_ALT_TEXT and HEADER_SALES_TEXT.
The defaults are
Code:
// added defines for header alt and text
define('HEADER_ALT_TEXT', 'Powered by Zen Cart :: The Art of E-Commerce');
define('HEADER_SALES_TEXT', 'TagLine Here');
The proper way to remove them is to remove the text between the single quotes, but leave the single quotes intact, so it should look like
Code:
// added defines for header alt and text
define('HEADER_ALT_TEXT', '');
define('HEADER_SALES_TEXT', '');