Correct. There is a licensing agreement. The STC shop first contacted me not long after I installed my GTN 750 in ~June 2013. There was a long wait for the licensing piece to get done. I believe Bendix/King also has one but then that is because Trig manufactures the Bendix/King transponders.
I have asked in passing whether this STC combo of TT21/GTN is only applicable to the current software version. I think the answer to that is yes based on my avionics shop's first guess without reviewing the actual STC language.
The explanation for the restriction, if true, would be that, in theory, Garmin could change its proprietary data format with any new SW version and that would render the transponder useless until it received an update. So the STC *may* be limited to SW Version 5.13 with further testing required upon upgrading to a new SW version.
Would be a good question for Trig if you don't want to try and find the STC itself. It should be in my records... which aren't here.