ITC refund

Utilizing LUT, we recently exported materials to Middle East countries (we are Chennai based company). However, our supplier from Bangalore charged us I-GST, despite we informed not to charge us as this materials are meant for export sales and we have LUT. Finally, we had to pay GST to supplier thought of claiming ITC refund for this export sales. We applied "GST RFD-01A" under "Refund of ITC on Export of Goods and Services without payment of Integrated Tax", which the local GST office indicated this refund claim not to be with GST, instead require to claim with Customs department. Is this true, as we never paid customs duty for this export shipment then how customs will refund against GST amount that paid to a supplier - please clarify.