Speaking at the Age of Ultron UK premiere, Elizabeth Olsen, who plays new character Scarlet Witch, said security was strict to prevent hacks.
Paul Bettany, who evolves from voicing Jarvis to becoming The Vision, said the script was never emailed to him.
Bettany told Newsbeat it was posted "with a security guard".
He said it had "a name all over every page so I couldn't tweet it... it had to be delivered into my hands".
Elizabeth Olsen added: "It was quite funny that we had to burn our sides for the day... we weren't allowed to go home with our little pages of whatever we shot that day.
"They took it from our trailers and shredded it. It's pretty crazy."
Chris Evans, who plays Captain America, told Newsbeat that most Marvel films are kept secret.
"Everything with Marvel is very lock and key and hush hush, you gotta sign a confidentiality agreement."
-BBC