Or better yet, stick it on the outside where it's guaranteed everyone will see it and its removal is almost a foregone conclusion (besides the written disclosure on the outside of the box and removal instructions in the manual). Then no will suspect you of doing anything underhanded.
Yours is the best solution so far. There is no reason to place it inside the gun anywhere if it’s just for inventory control. If it’s placed somewhere outside the gun it will be removed within the first 5 minutes it gets home. To hide it under a grip just makes more people uncomfortable and many will never find it. Non enthusiasts put the gun in a drawer and usually don’t clean it after use. RFID can be read at least from 5 feet away with no extra power amps and much much further if you really want to find one. The letter is too cute by half and tells lies to boot. That is absolutely a couple of names I will avoid.