The Greens are renewing their push for a federal corruption watchdog, as the political furore over the Sussan Ley travel affair continues.

The Health Minister has agreed to pay back some of the taxpayer money she claimed for several trips to the Gold Coast, although she insists her claims were within the rules.

Those rules have not been substantially changed since last year's inquiry into parliamentary entitlements, sparked by the Bronwyn Bishop 'Choppergate' row.

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Lee Rhiannon, Senator, Greens democracy spokesperson

Simon Birmingham, Education Minister