It is a common complaint about the app the presence of non thematic groups showing up. And I understand that any "choose your enemy" option is not viable for the app (its a development investment and not really desirable either), having to tweak the randomizer depending on the mission is a bigger development investment as well...
This is a "quick and dirty" approach that could help instead and I believe conveys a minimal development investment: Give th option to the player to re-randomize groups the moment the random groups pop up. Not even a button is required, just an option (to disable it for those that dont want it) and enable it somewhere inside the group info page, for extra point disabling the option once the group activates for the first time.