Removing featured image from gallery?

Assuming that you are using the standard functionality of the gallery:

You can extract the id of the images without having to do a query for attachments of that post
with:

preg_match('/\/', get_the_content(), $ids);

Then make an array of these values:

$ids = explode( ',' $ids[1] );

Eventually check if the id of the featured image exists and get its position( i think that it doesn’t exists till you don’t place it inside the gallery ):

$pos = array_search( get_post_thumbnail_id( get_the_ID ), $ids);

unset that value:

unset($ids[$pos]);

now you have all the attachments ids, less the one of featured image stored in $ids array.

UPDATE

<?php

    //// GETS OUR IMAGES
    $query_images_args = array(

       'post_type' => 'attachment',
       'post_mime_type' =>'image',
       'post_status' => 'inherit',
       'posts_per_page' => -1,
       'post_parent' => get_the_ID(),
       'exclude' => get_post_thumbnail_id(),
       'orderby' => 'menu_order',
       'order' => 'ASC',

    );

    $images = get_posts( $query_images_args );

    ?>

    <div class="sidebar-item not-in-responsive">

        <script type="text/javascript">

            jQuery(document).ready(function() {

                jQuery('#property-gallery-thumbs').propertyGallery();

            });

        </script>

    <ul id="property-gallery-thumbs">

    <?php

        $i = 1;     
        /// IF WE HAVE MORE THAN JUST ONE IMAGE
        if( $images ) : foreach( $images as $image ) : setup_postdata( $image ); ++$i;

    ?>

            <li class="thumb<?php if($i==1) { echo ' current'; } ?><?php if($i%3 == 0) { echo ' last'; } ?>">

                <span class="hidden full"><?php echo wp_get_attachment_url( $image->ID ); ?></span>
                <span class="hidden main"><?php echo ddTimthumb(wp_get_attachment_url( $image->ID ), 680, 450); ?></span>
                <span class="thumb"><img src="https://wordpress.stackexchange.com/questions/109068/<?php echo ddTimthumb(wp_get_attachment_url( $image->ID ), 76, 76); ?>" alt="<?php the_title() ?>" title="<?php the_title(); ?>" /></span>

            </li>

        <?php endforeach; wp_reset_postdata(); ?>

    </ul>
    <!-- /#property-gallery-thumbs/ -->

</div>

    <?php endif; ?>

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