I know there is confusion on where the tag is placed because I've had it done both ways as well. IMO, the tag goes outside the hardcase for the gun, not inside with the gun. Maybe they can see the tag with the xray no matter where it is located?
But I'm not going to take the risk of missing a flight or being called out for improper baggage due to the TSA and being told incorrectly. When I show up at the airport, I ALREADY have a filled out tag both inside the hardcase with the handgun and outside the hardcase near the gun case. These are old tags with my name/address and today's date but without the endoursement. Then I fill out a third tag at the counter and place it wherever they like but they never ask me to remove the old tags and I'm covered.
Keep your old tags and use them as long as you have declared your firearms unloaded today. But always use them in conjunction with new tags.