The inquiry wants to know why the government granted the six-year funding stream to the small not-for-profit foundation in a meeting that lasted less than an hour.

Labor has written to the former prime minister asking he return to Canberra for questioning.

Foundation directors, including chairman Dr John Schubert, were grilled during a three-hour hearing at parliament on Tuesday.

Dr Schubert told the committee the first he knew about the foundation receiving near half-a-billion dollars was in a meeting with Mr Turnbull and then-environment minister Josh Frydenberg in April.

The Sydney meeting was arranged only two days before and no information was given prior to what it was about.

"The idea that you can go to a meeting, with no paperwork, with no agenda and within half-an-hour you've got $444 million - you couldn't write this stuff," Labor leader Bill Shorten told reporters on Wednesday.

Dr Schubert said the foundation recognised that climate change is the biggest threat to the reef, believing it had already been "altered forever".

Despite this, he said it was not the foundation's place to take political positions on other projects that could contribute to climate change, including the proposed Adani Carmichael coal mine in Queensland.

Foundation director Grant King has expressed his support for the Adani proposal.

Labor senator Kristina Keneally, who fired questions at the foundation directors on Tuesday, believes there are too many unanswered questions for Mr Turnbull not to appear.

"We have written to (Mr Turnbull) - we have respectfully asked for his participation," Senator Keneally told reporters in Canberra on Wednesday.

"The concern here is that there was no process to say that this was the best use of the money."

Australian Associated Press