"Zuzu's petals" is a phrase from the 1946 movie It's A Wonderful Life which since its release has become a Christmas season film classic.
The petals belong to Zuzu Bailey, the youngest daughter of George Bailey the main character. Early in the film, Zuzu shows a flower that she brought home from school and became upset when the petals started to fall off. Her father pretended to reattach them but actually just slipped the lost petals into his pocket.
By the end of the movie, after considering suicide, George has been shown what the world might be like if he had never been born. Given a second chance by God, aided by the angel Clarence, all the changes he had seen in the world were undone. His first realization that his world had been returned to him was when he found that Zuzu's petals were once again in his pocket.
The phrase has become a kind of shorthand way of reminding people of the hope that things can be mended and made better.
"Zuzu's petals...Zuzu... There they are!"