The first screenshot is not Dugi Guides. This looks more like a World Quest addon, I can’t really name it because there is more than one addon that specializes in World Quests. I use Angrier World Quests myself.
    The second screenshot is Dugi Guides, if you click the binoculars on the mini map and then un-tick Track Pets, that should remove the pets from the maps.
    This can be ticked if you want to track the pets when you do pet battles.