Hi @ The_Interphaser,
You absolutely do not delete them or even reverse them. As Eric3 said you do a negative sale for the amount inclusive of GST, and make sure the tax code shows as GST.
If the realisation that the debt will not be recovered in the same financial year that the sale occurred then you would just allocate the amount to the sales account. If the financial year the sale occurred in has finished then you allocate it to bad debts expense account.
Depending on whether you are Cash or Accruals basis for your BAS as well as for your income tax, you may have already sent this GST off to the ATO and also paid Income tax on the amount.
Some business are cash basis for GST and accruals for Income Tax.