You could try modifying your query such that you have an array of categories to exclude and a conditional in the foreach, working similarly to the !empty(). An untested example:
<!-- category list with thumbs -->
<?php
$terms = apply_filters( 'taxonomy-images-get-terms', '', array('taxonomy' => 'category') );
$exclude = array(1,7); //add the category IDs to exlcude here
if ( ! empty( $terms ) ) {
foreach( (array) $terms as $term ) {
//check the category's ID and output code
//if it's not in the $exclude array
if ( ! in_array($term->term_id, $exclude) ) {
echo '<div class="issue clear"><h3><a href="' . esc_url( get_term_link( $term, $term->taxonomy ) ) . '">' . $term->name . '</a></h3>';
echo '<div class="grid col-120 hide"><a href="' . esc_url( get_term_link( $term, $term->taxonomy ) ) . '"><img src="IMG SRC" alt="" /></a></div>';
echo '<div class="grid col-780 fit">'. $term->description . '</div></div>';
}//if in_array
}//for each
}//if empty
?>