No. Being ONLY the second owner and having paid the fee, you are warrantied just the same as the 1st owner. For $110, I would be on the phone to Chrysler asking why you had to pay. That TSB thing was a "surcharge" and was limited to $65 as I recall.
Please call and ask-I'd really like to know, as would everyone else.
Here you go:
https://www.crossfireforum.org/forum...-tsb-work.html