Thinking back 34 years, I don't recall exactly when the Team Tornado badge was issued to those on the conversion course at TTTE (Crew solo, end of course, e.t.c), but in my time at Cottesmore I don't remember seeing any badge unpicked.
Commercially, the only version I've ever seen for sale is the version with no wording on the bottom, but I was told at TTTE that this was effectively a copyright issue - whether true or not, I have no idea.