On Wednesday, it took authorities 10 hours to discover that the device attached to 18-year-old Madeleine Pulver was not an explosive.
A note of demands had been attached to the device, officials said, though they did not specify what the demands were.
Pulver lives in Monson, which is an area some people call the Beverly Hills of Sydney.
Pulver told police a man wearing a mask broke into her home and confronted her while she was in the kitchen.
The teen said the man forced her to stay still while he fitted the device to her neck, and then he fled.
Detectives are investigating whether her father, a wealthy CEO, was the target of an extortion plot.
Pulver's family said Thursday that they're proud of her.
"I can tell you that we, as parents, are extraordinarily proud of Maddie. I think she is waking up this morning in pretty good spirits. She is a little tired, a little sore from holding this damned device in place for about 10 hours but she is now, as we are, eager for her to get on with her life," said her father, William Pulver.
Madeleine Pulver was examined and released from a Sydney hospital on Thursday.
Counseling is being offered to students at the private girls' school she attends.
The Associated Press contributed to this report.