This is the semantic linkback plugin. It adds more context to pingbacks. If the site linking to your site has microformats more info may come along
Thanks Matthias Pfefferle
I do wonder if theme develops could add this functionality native or just recommend an install.
It does have a mf2 parser and those are actively developed so a plugin may make more sense.
If you want to build an #IndiWeb Theme you need an h-card on the homepage. This is your business cars. People often put them in the header or the footer.
You can also use the IndieWeb plug in from David. Shanske. That uses the profile page and has an h-card widget