The children had applied to be contestants on a new television show called 'Gastronauts'.
Work on the show, which is being made by Objective Productions, was temporarily suspended while the theft was investigated, but will now carry on. Reports say that the stick was stolen from an employee of Objective, but that there has been no evidence that it was misused.
Richard Deverell, who is controller of BBC children's programming, wrote to the parents concerned. He said: "I offer you my sincere apologies and my assurances that we are taking all action possible to mitigate the consequences of this regrettable incident."
A helpline has been set up for anyone concerned about the lost data.
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