When you receive pieces like bonus stamps or pets baskets, you can manage them in the Piece Factory. Follow these steps to find it:

Tap your avatar on the top-left corner of the game lobby to enter the Profile section.
Select "Backpack" from the available options.
In the Backpack, choose "Pieces" to access the Piece Factory.
Here, you can view your collected pieces and combine them into completed ones once you gather 100 pieces. Enjoy managing your rewards!