So, my webmention issues can’t be solved in the theme, as the content isn’t decided there. I need to dig deeper into the semantic-linkback plugin that I use to handle them.
I found out that webmentions are mentioned in full if they are short enough, and that I can set that limit. So I now want to change the way webmentions are stored. To solve my main issue, I need to select x characters around the spot where my site is mentioned, and set the character limit for webmentions to x+1.