If you were offered a course with TTC then it will be on file with us, even if you did not actually do a course. If you were offered one but chose a different provider then they may have it on file as well.
the other option is to contact the court, but they will not search for the conviction, you have to tell them the actual court date and they will look at that day only. They will have your conviction, with the fine and the length of the ban.... hopefully they will have recorded your reading in the court register as well.
You need to find a letter or envelope that has been sent from TTC. On it will be your reference number. Call them with the reference number and the office staff will be able to give you the details that you want.