Hi, many people have reported issues since the upgrade and in every case it was caused by an error in jQuery from a theme script. And a theme update to make it compatible with jQuery 1.12 fixed it every time.
However, in your case it's not so clear.
I do see in your source code that you are including the jQuery library 5 (five! in different versions!) times:
http://veneers.com/wp-content/themes/brookside/effect/jquery.js
http://veneers.com/wp-content/themes/brookside/js/jquery-latest.js
http://veneers.com/wp-content/themes/brookside/js/jquery.max.js
http://veneers.com/wp-content/themes/brookside/js/jquery.min.js
http://veneers.com/wp-includes/js/jquery/jquery.js?ver=1.12.4
This should be just once. Preferably just the one included in WordPress (/wp-includes/js/jquery/jquery.js) ... Every additional loading of the main library is asking for trouble and makes debugging practically impossible.
Here are some resources with instructions on how to include jQuery in WordPress:
https://digwp.com/2009/06/including-jquery-in-wordpress-the-right-way/
http://stackoverflow.com/a/22239396/573224
Long read (but instructional) https://premium.wpmudev.org/blog/adding-jquery-scripts-wordpress/
Official doc https://developer.wordpress.org/reference/functions/wp_enqueue_script/
I suspect after cleaning up all redundant/double inclusions of the jQuery library, the close button issue will be gone... If not, please let me know and I'll try to debug further.