The thieves stole the bright yellow Big Bird costume - worth $160,000 - earlier this week but returned it undamaged early on Wednesday morning.
They left behind a note, saying they didn't mean to cause such trouble.
"We were just having a rough time and were trying to cheer ourselves up," they wrote.
"We had a great time with Mr Bird. He's a great guy and no harm came to our friend.
"Sorry to be such a big birden (sic).
"Sincerely, the Big Bird Bandits."
Police said the letter was found in Big Bird's beak after two men were spotted running from the scene.
Patrols searched the area using a police dog but the men weren't located.
The investigation into the theft continues.
Main images: SA Police.