Hey there,

I am really sorry for the delay of this reply as it is a weekend for us here.

As long as that is group member, they can able to see those task stream item on the user dashboard page.

And the only way to hide these thing is :

1. Admin disable those stream item from the task group app (screenshot : http://take.ms/iNbNQ) but it also will hide it from the group stream listing page as well.

2. If the group member feel annoying when always see these task stream item, they can able to hide this these similar stream from their personal account. (screenshot : http://take.ms/HzaIA ).