dodgy comments as pingbacks

Hi, I have been looking for help with this issue already at the theme developer and I was advised to ask you what it could be. The problem I described was:

Every time I create a new post which contains a link to another of my posts, a dodgy message appears in the comments about the post I referred to in the link.
If I link these posts mutually together to each other, two messages appear in my comments list, for each post (or the associated link to the other post).

The theme developer said this:
“Because this problem come from the core wordpress script, I’m not sure why you got that notification. Since WordPress 4.x the wordpress developer have change so many core code. I think you should ask this question in forum wordpress.”

I am running my website on www.ads-software.com, just for sure. The pingbacks do not show as some notifictions, but as posts, which I have moved to trash instantly. And those two boxes were left blank: https://i.imgur.com/I4dMzmn.png

Any ideas?