I did as instructed, created the link-library-images directory, gave it 777 permissions, and generated the thumbnails. When I did that, I received a bunch of errors (guessing one for each link on the site) that said:
Warning: file_get_contents(http://open.thumbshots.org/image.aspx?url=https://taxpackagesupport.com/(S(2wso4w45g2whrbq1ro2f5zrf))/k1SupportHome.aspx) [function.file-get-contents]: failed to open stream: no suitable wrapper could be found in /home/content/t/k/t/tktcpa/html/wp-content/plugins/link-library/link-library.php on line 360
Line 360 of my link-library.php file is "$imagedata = file_get_contents($genthumburl);" The link-library-images directory now has files in it but they are all 0kb. I unchecked the "Use Thumbshots.org for dynamic link images" box and loaded up the site and now there are no thumbshots at all (which I expected since the files are 0kb) but there is still a delay.
I left the site like this so that you can see it - http://www.tktcpa.com/links/. Debug mode is still on.