When you download Osmo Masterpiece and launch the game for the first time, a message will pop up saying "Masterpiece would like to access your photos". This allows Osmo to access your photos so you can use them to draw in the app.
If you tap 'Don't Allow', the program won't be able to access your photos. However, this also means that you won't be able to draw Masterpieces using your own photos.
If the app is currently installed, you can change this setting by going to Settings > Masterpiece > Photos and then selecting either 'Never' or 'Read and Write'.