(This is a much better question for @sphygmus, who seems to have a dope Webmention setup for her TiddlyWiki.)
Webmention in general is certainly dope.
In looking at her set up, it looks like she's used her site to sign into Aaron Parecki's https://webmention.io/ service which gives the site two link elements to put into the <header> of the site. Webmention.io then does all the plumbing for the site and allows you to log into a dashboard to see your notifications. Signing in only requires adding rel-me links from your site to at least one service (Twitter and GitHub are common) that links back and can do the oAuth dance on your behalf.
I've know this was possible for sites that didn't have plugins or custom code yet, but hadn't done it until I added it to my own MediaWiki site last night.
If I recall, there's also a way to use some scripting to export the data from webmention.io to display it on your own website, but I haven't gotten that far yet.
I suspect this is what @sphygmus is doing, though she can confirm.