In my best knowledge, it will depend how you show your income from this booking.
i.e, if your rate is $100, you receive $85 from Expedia (15% commission ).
If you show the income as $100 you would claim the $15 as a deductible amount against your income.
However if you, as we do, show the NET room income as $85 there is no claim for commissions.
The same rule would apply to any GST component.