They know only Sebastian in Alpha team knows about this matter, which means the situation isn't completely out of control, yet. Sebastian is too simple for his own bad, they can use the gamma team as bait to control him.
Since except for Sebastian no one knew what made him begin the investigation in the first place. So, they ended up ignoring the why and focus on how. How can they prevent their shit from getting out of control? They keep gamma teams' every move under their strict supervision. It's not like they didn't prevent the gamma team from extracting information or add hurdles in the gamma team's way.
But the gamma team was too skilled for their own good and went to the bottom of every single detail given to them, leaving nothing behind. Well, the gamma team wouldn't have been captured, if the thugs would have attacked in the daytime. It's not like they can't stay alert at night. But they have just passed the complete information and have completed their mission.
