(ב) אם טעה המזמן-בעשר' והעוני', ולא הזכירו "אלהינו", אין יכולים לחזור. 1
אבל אם עדיין לא ענו אחריו יחזור ויזמן בשם: 2
If the leader of a 10-person meal, along with the participants all forgot to say the prescribed "Elokeinu", they cannot retake the zimmun.
But, if the leader caught his mistake before the participants began their recitation, the leader can restart the zimmun correctly.
1 In a scenario where both the leader and the participants forgot Elokeinu (i.e. the case of the Shulchan Aruch), they cannot retake the first refrain of the zimmun.
However, there is a shayla in the Poskim whether the leader can say "Elokeinu" in the second refrain of the zimmun.
In a scenario where the leader forgot but the participants remembered to say "Elokeinu", all Poskim concur that the leader can say "Elokeinu" for in the second refrain of the zimmun.
2
When the leader catches himself before the participants answer for the first refrain, the leader can restart because so long no one answered his initial zimmun call, the Halacha doesn't see the zimmun as even have started, and therefore he can do a retake.
But once the participants answer, we see the zimmun as being in progress / complete, and it is too late to undo a zimmun which was already accomplished.