The paper work didn't look like a request, just a statement of fact.
Also the lawyer's explanation showed that she was under extreme duress at the time, and was unable to contact and discuss the matter with the father.
ICE had her and her child detained, they offered to send her child out of the country with her as they were forcibly deporting her, we don't know if they offered to send her child back to the father.
They gave her a pre written letter to fill in the blanks, did they have a pre written letter that allowed her to fill in the blanks and let her child go back to her husband? Would have she been afraid that her child would have got lost in the system and she wouldn't see her child again for years or forever, just like what happened with people in the Separation at the Border policy of Trump's first administration?