TDs on reimbursement of conveyance

Dear Sir/Madam,

We paid travel reimbursement to staff who has hired private vehicle from residents to office to residents through car hire services provider.

Staff have paid directly amounting more than 1 lac to the car service provider through their pockets.

In that case, can company deduct Tds on hire car by company.

If Yes, on which basis and for which any notification or If no then why not deducted Tds

Please clarify