Had the same issue a few years ago. Telstra couldn't give a toss. You have to ring them and get the service disabled. Virtually every other carrier has it disabled by default, but not Telstra, they wouldn't want to miss their cut.
I got charged 90 bucks for it. I didnt even know it was happening until my normal bill was way higher than usual. All Telstra would do is provide me with a phone number to complain to that was supposedly the contact number for the company involved. all I ever got was a recorded message, never a real person.
Rang Telstra back and said I had not authorised the costs, I had not signed up (I had a nokia 3310 at the time, so no MMS capability anyway!). They refused. I said you sure about that, I have been a loyal customer for more than 20 years? They said they would do nothing for me. I said fair enough, that's your call.
So I proceeded to move all my family mobile phones (3 kids phones under my name as well as my own personal and work phones) and my house phone and my internet service to other suppliers. Their refusal to sort out $90 worth of fees I did not incur cost them probably over $2k a year in business, been at least 5 years now, so 10k and counting.
I will never do business with Telstra again. They rang me several times asking me why I left and all I did was say you know perfectly well why, you ripped me off by $90. All sorts of pleas and deals offered to get me back, but never a refund of the $90.......