Witt had sought more than $13,600 for the costs it incurred fighting the case, according to the latest decision, released today.
It hired three handwriting experts to examine the letters it suspected Parr had written.
Parr questioned why she should be subject to a further financial imposition given the penalty already imposed on her was "global".
"She then says the substantive outcome was, at least in part, based on my having made incorrect assumptions," said ERA member Mike Loftus. "She claims the outcome was harsh and that should be taken into consideration."
Parr had also noted she was out of the country when Witt initially sought a response that might have avoided litigation. She added she was a superannuitant and was not in a position to pay more.
Loftus was not persuaded by Parr's arguments.
"She says costs should not be used to punish other than to the extent they were unreasonably increased by a party's behaviour," he said.
"She is correct but the punishment aspect was addressed via the penalty. It was global in that respect but did not address costs, which are a separate consideration and normally follow the event."
There was no evidence supporting her claim of being unable to pay.
"To that I add knowledge of the original settlement [details of which are suppressed] and the fact Mrs Parr can still afford overseas vacations. That argument, as presented, carries no weight," Loftus said in the decision.
He ordered Parr to pay Witt $5700 by October 30.
Parr has maintained that she did not write the letters, which in 2013 resulted in her leaving her job of six years as a result of a personal grievance application.
That was resolved through a mutual agreement, which included the condition that she "not make any negative or disparaging statement publicly about Witt or any of its officers or employees", according to the earlier ERA decision.
When Cunliffe and Joyce received the letters, Witt management hired three handwriting experts, one of whom, senior police document examiner Patricia James, concluded: "The author of the specimens attributed to Angela Parr completed the address on the questioned envelope and the printed entry at the top of the questioned letter".
Parr argued that letters sent to ministers should not be considered public and therefore did not breach the 2013 agreement.
After the initial decision, Labour's tertiary education spokesman Chris Hipkins accused Witt of engaging in a "witch hunt".
"Members of the public should be free to communicate with Members of Parliament without the fear that they will find themselves in hot water. It's an important part of the democratic process," Hipkins said.
"I'm concerned that Witt have gone to the lengths of engaging handwriting experts to identify the author of the letters. Whatever the contents of the allegations, as a public institution they should be willing to answer them rather than conduct a witch-hunt to find the person making them."
