Johansson and her Island co-star Ewan McGregor's acting skills were blamed by producers after the action thriller failed to reach box office expectations.
In a recent New York Times interview, Johansson talks about her love of on-set gifts and her pet Chihuahua.
She says, "On the set of The Island. Ewan McGregor gave me coats and collars and lots of dog toys."
After mentioning Bay has huge pet dogs, Johansson adds, "He needs them. He has a lot of enemies."
When asked if Bay gave her any presents on the set, Johansson laughed politely, but did not elaborate.