A couple of days ago I posted this about one of our rose bushes. Publishing for help on the Internet works. I got two links from friends, one in the U.S. and another in Germany.
One of my German readers (Micha) identified it as Wildtrieb and here is an elaborate description. Sorry, this is quite technical and I could not find any suitable translation. One of my American readers (Jane) also referred me to a related article: Here is an English equivalent, they are called suckers.
Both articles clearly spell out that the suckers need to be removed, otherwise they take over the plant and eventually destroy it. I’ll be out there tomorrow pruning it down.
Thanks to my readers! Mystery solved.