Well, I've posted over there about this issue more than once, deleted these marketing shortcuts several times and did so one last time, opened the start page again, left the shortcuts alone after they reappeared again, closed the ASB browser and left it alone for a few days. I was surprised when these shortcuts did not appear again and haven't seen them since.
Happy to report no more issues with these shortcuts. Gone.
Now if Avast can kindly let us know when ASB has been updated and where the changelog is, we'll really be going to town.