Two girls, aged 13 and 15, and a 13-year-old boy were handed the biscuits on Freeman Street on Saturday evening, police said.
The teenagers were treated at the Diana, Princes of Wales Hospital and later discharged.
A 60-year-old woman arrested in connection with the incident has been released on bail until early November.
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Detectives said it was "too early to say exactly what has happened".
Det Ch Insp Nicki Miller said: "[This] should serve as a timely reminder to people and I would encourage parents to remind their children that they should not talk to people they don't know.
"If they are approached by someone who they are unsure about they should alert their parents who in turn should contact the police if there are genuine concerns about them."
Three children needed hospital treatment after eating cookies given to them by a woman in Grimsby.