Although embattled MP Craig Thomson's political career is apparently on a downward slope due to the Fair Work Australia (FWA) report that he misused $500,000 of Health Services Union (HSU) funds, it is not only the legislator whose reputation has been damaged.

FWA President Iain Ross told a Senate committee on Tuesday that the investigation has also exposed confusion over the organisation's role. To address the problem created by the Thomson probe, Mr Ross proposed changing FWA's name through legislation and for more clarity on the role of the agency's tribunal and its administrative unit.

He also said that FWA Vice President Michael Lawler, the partner of HSU current National Secretary Kathy Jackson who is also the whistleblower, denied the charge of Mr Thomson of misconduct. Mr Lawler insisted that the MP's accusations are false.

Mr Thomson, in his statement to parliament last week, accused FWA investigator Terry Nassios of being selective and biased. In defending Mr Lawler, the FWA president reminded that the former is a judicial officer who took an oath to faithfully and impartially perform his office's duties. He stressed that only parliament could boot a sworn judicial officer.

The Senate recalled FWA officials who finished providing evidence on the Mr Thomson on Monday after Coalition Senator Eric Abetz disclosed that he has evidence that FWA had evidence three years ago of problems in the HSU which should have been referred to the police.

The senator referred to a 2009 memo from Doug Williams, who then headed the FWA predecessor - the Industrial Relations Commission (IRC) - that suggested referring the HSU problem to other authorities. The memo was addressed to Mr Nassios, who also investigated Mr Thomson.

Prime Minister Julia Gillard has denied that she saw the email from IRC three years ago. She urged the Opposition and parliament to move on with the Thomson case and to concentrate on other more important national issues.