The app developer resolved my question so ít was perhaps premature of me to post here but for what's it worth here's the reply in case it can help someone else in a similar situation.
"Hi Claes, not to worry, I’ve seen this before. What is happening is that when the Automatic Connection Testing feature is turned on in Network Logger Pro, it makes http header and pings requests to the top 5,000 servers on the Internet. A few of those URLs are blacklisted and I’m assuming that your Avast app has such a URL blacklist. I’ve been removing blacklisted URLs from the testing list as people bring them to my attention. However, even when present, no payload data is downloaded from those servers, Network Logger Pro is just seeing if it can reach them in the course of checking to see if your Internet connection is up. In short, the program is fine. Thank you for that screenshot, I will remove that URL from the list for the next update. Feel free to forward any others you encounter."
Best,
Claes