From Halachos of Brachos by Rabbi Pinchos Bodner (pg. 125)
When a person make preparations to Bentch. His preparatory action strongly indicates that has ended his meal or eating session. Therefore as soon as one start preparing to Bentch, Even though he did not as yet to begin to recite it. According to many opinions (S"A Orach Chaim 179:1) is considered a hesech hadaas, and thus, his brocha rishona ceases to be valid and you will either need to make a new blessing or bentch.
However when one is a guest at another one table, the host rather than the guest determines when the meal or eating session terminates. For example if the guest started preparing to bentch But the host was not ready to, The eating session Did not terminate. Also, If the host says lets bentch, since the guest room is dependent on his host for his food the host decision to terminate the meal causes it to terminate for the guests as well.
Furthermore, washing the hands after the meal is according to many poskim considered a termination as it is a sign that you desire to bentch (M"B: 2), So too is lifting the cup of wine as it is similar mayim achronim (S"A seif 3, M"A s'k 5). The Tur though, does hold that one may continue to eat after mayim achronim as it is not necessarily a sign of preparing to bentch. However, the Magen Avraham (2) writes that being that this is a dispute among the poskim, one should be stringent to bentch right away.
Seemingly, according to the above quoted, picking up the bentcher when their being passed out to bentch could be considered a preparation for bentching and in order not to enter into a dispute among the poskim one should bentch.
So too, if you were unsure if you finished, this as well is a dispute and thus one should also be machmir and bentch right away.