In his affidavit, Timothy Blake said no application had been made to have the order of Cork Circuit Court of 2001, in which the boy was made a ward of court and the Blake grandparents were given joint custody, discharged or varied.
His daughter did not comply with that order to return the child to Ireland.
Mr Blake said he could not understand why the Irish authorities were applying for his extradition in such circumstances.
"We were giving effect to an Irish court order. We would never do anything to harm a hair on his head."
Given cardiac, diabetic and other medical problems, Mr Blake said there would be little prospect of him leaving prison if extradited to the US. His constitutional rights to fair procedure, bodily integrity and liberty would be breached, he said.
In her affidavit, Ethel Blake said the boy had been returned to the US in settlement of court proceedings. She and her husband had agreed to this to minimise the stress on their grandson.
There was now contact between the two families and they spoke to the child and his mother on the phone every week, she said. No members of the family, including her daughter, wanted the extradition to proceed.
If extradited, Ms Blake said she was advised securing bail would cost some $2 million.
She was terrified of what would happen to her if she was sent to the US, Ms Blake said.
In other affidavits, a number of medical experts said Ms Blake could suffer a severe depressive reaction if extradited and incarcerated. It was also stated she could suffer deliberate self harm that could be fatal.
The case continues today.