If you can't set a class for each link that has an image inside of it, you prolly must use javascript. You could simply add something like this:
jQuery(document).ready(function($) {
var a_with_img = $('a').children()
$(a_with_img).parent().css('text-decoration', 'none');
});
This should work, however it's never a good idea to target all the 'a' selectors with js, it's pretty heavy on the load. Might cause slowdowns to your overall pageload.