Actually, what you want to do is possible:
After you do a search, move all those references to the new group you’ve already created. They’ll be showing up under search results, so you can’t “Remove references from Group” because you’re not really in a group.
Click back into the original group and you’ll see it jumps you to the first reference from your search results. It will be highlighted in light gray. The other ones are also still selected and highlighted in light gray, but probably further down in the list where you can’t see them.
If you just right click on that first reference, you can select “Remove references from Group” and it will do that for all the references from your search results. You just have to be in the original group they came from, not the search results window.