It may help if you change your terminology to "allowance" instead of "reimbursement". A reimbursement is for actual expenses incurred (e.g. a flight, tools, etc), whereas if you are paying staff $x per km, that's an estimate to cover costs - which is an allowance.
Allowances don't attract GST because they are wages. Because they are wages, the amount received by the employee is taxable and should be on their group certificate.