The code is hard stored into the memory in the ROM of the ECU. Trust me I know and bought the BavTech tool to clear it and reset the adaptive's. You got lucky to get your emissions to pass before it popped back up.
I could get it to pass again if I wanted to lol, It seems if I clear the code I get ready status in a day, then one or 2 more starts from there the 2096 appears. I have been debating on buying the tool seeing I have an airbag light on that needs to be addressed as well, guess it will pay for itself pretty quick.
Looks here, option 3, for a single car. $179.00 Bavarian Technic Software - Products for sale I have the Enthusiast kit - option 1 $287.00 and I have used it on many friends cars. (Over 10 +) It says it has a 3 car limit but if you never register a car it unlimited.