I guess it's not image logo, it looks like text. Take a look at following two divs:
<div class="newsletter-title">...</div>
<div class="newsletter-slogan">...</div>
This probably represents the place where it's generated. You can change it by finding where it is generated (probably somewhere in Magento Admin), or change it directly. If you want to use any kind of image, you can put it directly as (for example):
<?php $imgLogo = Mage::getBaseUrl(Mage_Core_Model_Store::URL_TYPE_MEDIA) . "/logo.jpg"; ?>
<div class="newsletter-title"><img src="<?php echo $imgLogo ?>" class="imgLogo" /></div>
Then you should modify your CSS in order to fit image properly. Or you can just change text, without any other modifications, something like:
<div class="newsletter-title">My new title</div>
<div class="newsletter-slogan">My new slogan</div>
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