You need not worry. This is more of a fiscal requirement rather than a change of procedure to the guest. Argentina has several types of invoices depending on the type of consumer and type of seller... A, B, C, M, E... now for the hotel VAT refund, hoteliers AND local travel agents who refund VAT, need to give guests an invoice with the letter T.

There are still quite a number of problems to be solved, so I would recommend that you ask for the invoice to either your Argentinean travel agent or the hotel, and if they do not produce it, be certain that you are not charged the 21% VAT. Remember payment can only be done with international credit/debit card or international wire transfer.
If they give you the VAT refund by paying cash of any sort... well no need to explain...

Hope I have shed some light.