Judge Jeremy Richardson QC adjourned the case for two weeks because he wanted more time to think about what sentence to pass.
He said he was thinking of either sending Jackson to jail or on a sex offenders’ treatment programme.
Speaking outside court, the girl’s mother said: “His sentence should be prison.
“He shouldn’t get off lightly with a course. I want him to have some comeuppance.
“My daughter is terrified; she’s too scared to go out.”
The court heard the theft took place between February and March last year after Jackson was given the PIN for his grandfather’s bank card when he did an errand for him.
His stealing was discovered when he tried to make a withdrawal from a Santander bank, and staff became suspicious and refused.
His family were informed and found the bank card was not where it should be, and Jackson admitted what he had done.
It emerged he had been withdrawing £250 a day for about four or five weeks.
John Thackray, prosecuting, said: “He said he used the money to buy things for his friends, and apologised and offered to pay some of it back.”
The judge told Jackson: “Luke Jackson, you have many disadvantages in life.
“But you have done wrong and ordinarily prison would follow but I want to give a second thought to it.
“There are some very unusual features of this case, exceptional features, and thus I want a little time to think about what is to be done.”