Migration issues

I migrated content from Typepad to WordPress 3.3.1 using using movable type and Typepad plugin from one domain to another.

I thought all of the content migrated over properly. When I use the plugin LinkWithin, that directs users to content that is considered similar to individual blog post on the new site, it directs users back to blog post that are located on the old site not the new site.

If you go down to the bottom of the page you will see the LinkWithin links on the page.
https://vintageconsignor.com/2012/02/smithsonian-libraries-presentsgeorge-dyson/

How can I get the links to stay on the new site?

Thank you for your assistance