I purchased a new suitcase last month in Lisbon and flew out on TAP. This is the process at Lisbon airport that I had to follow.

1) check in with airline and inform them one of your bags is tax free. They will tag all of your luggage to your destination then return the tax free suitcase to you with the tag attached and put the other bags down the belt to be loaded into the aircraft.

2) take the new bag only (as the other bags are now on their way to the aircraft) with your boarding pass, passport, receipts and tax free forn to the tax free area. It’s a different check in area with both customs and a baggage collection point. It’s not the easiest to find so make sure you get the counter number. It took me about 10 minutes from the TAP check in area. Customs will stamp the document and the counter next to them will take the bag and place it onto your flight.

3) I used the refund counter after security and with the receipt, customs stamped tax free form, passport and boarding card in hand the refund took 5 minutes and was paid in cash against a small fee. My receipt was issued by global blue. I’m not sure if the same refund counter took other companies receipts or not.

its possible you may have been issued a receipt encouraging you to use their barcode scanning passport scanning machine. That’s always an option but I wouldn’t feel comfortable and preferred to just get the stamp as the line is usually empty before security.