What would have happened if anne marie had not gotten the handkerchief to uncle henrik?

I believe the answer is: The Rosens and other Jews would have been caught by the Germans

In the story, the rosens and the jews have to hide at the bottom of the boat while the nazis were searching for them with hunting dogs.

The handkerchief that held by annemarie messed up the dogs' sense of smell and make the nazis failed to get them.