Once you give it back to him, he will lift his club, allowing you to proceed and go to his garden.
Trivia[]
The Golden Egg and its status of belonging to the Purple Giant is a reference to the fairytale of Jack and the Beanstalk.
In the fairytale, the Golden Egg is stolen by Jack - purveying that it was stolen from the Purple Giant. A candidate could be the Green Explorer, as he apparently explored the skies.