In Minecraft, to place the Pup Badge in the Lookout on the Pup Screen, you would need to use an item frame to display the badge. To create the Pup Badge, you typically would use specific items in combination, but make sure you are following the correct in-game process.
If you are specifically talking about a mod or an update with unique mechanics, please make sure to refer to the details of that mod or consult the latest Minecraft guides, as mechanics can change over time. However, for the standard mechanics in the base game, placing an item in an item frame is generally how you would display badges, decorations, or any item in significant places like the Lookout.
If you are referencing a specific quest or challenge related to a popular mod or adventure map, please provide more details for precise instructions!