From the comments Nothing in your analysis shows this. Moreover unless you explicitly deployed a root certificate on your clients (or if an app on the client did it), the router can't decode TLS traffic (deep inspection) without you getting certificate warnings on the client. In that case, the only thing the router can see is the dns request, the IP and the TLS SNI. In short your title is misleading. permalinkembedsa…
... and I don't get your point in this useless pedantry? Sure that the data in of itself is not sent, but you seemed to imply that DNS queries don't reveal anything. In practice, you can build a good enough picture to decode what's their interests, what type of places they visit etc., which is worrying of itself. It's like saying to not worry because they didn't know you ordered a Big Mac while the fact that you went…
I agree this is tremendously bad code, but what they observed could also be perfectly explained with "some stupid code doing a Avira subscription check whenever something arrives at the router and they do that without a cache for negative answer, and even if the feature is turned off".
So we need more evidence.