The bird was found on an airliner
Its cage got broken as they cleared the plane and it flew through the gate. They caught it without any bad incident and everyone fondly remembers that day. They brief the passengers they take
The passengers were told why they had been taken and they all understood it. That's why they calmly shuffle to the gate when told to at the end. Using Time Travel to stop whatever polluted the world has already been tried, and it failed.
They decided to risk the timequake and remove whatever fouled the Earth, but it didn't work. They can't go back to those times now to try again.