As AJ suggests, the simple solution is to instruct your bank to reverse the charge to your account. Whoever originated the transaction then has to evidence that they hold your authority to make the charge or take it back, effectively put up or shut up.
It is possible for organisations to originate such charges and payday loan companies in the UK frequently use them. Rather like a merchant trader facility a finance company allows them a facility and undertakes to make refunds in response to mistakes or fraud. On one occasion such a company in the UK was originating charges to people's accounts in response to fraudulent applications by criminals and they didn't hold any proper authority. There was quite an uproar and the company folded, after all victims had been refunded.
The circumstances were daft as the pdlc was accepting ID details anyone could get hold of, and to compound matters, was then sending the money to a different account to the one they were charging.
I can't say that this is what happened in your case, but it has similarities. However in any event your primary recourse is to your bank who must justify why this charge has been placed to your account. If they can't, they must reverse it.
Don't be rude to your bank, but be firm.
Don't go chasing after companies you know nothing about and with whom you have no relationship. Your bank allowed the charge, it's for them to clear it up and obtain reimbursement if it's unjustified.
It's a bit of bugbear with me that simply knowing someone's account details doesn't give them the right to pass a charge. If you could, with my background in banking, I'd be a multi-millionaire. Anyone you give a cheque knows your account details and has a specimen of your signature too, but think of how many utility companies, shops, catalogues, local tax offices hold this information.
Merchant trader facilities and other similar arrangements should only be given to very reliable and trustworthy companies, because the implications for those that hand them out can be catastrophic if they're misused. I've come across instances in the UK where the system hasn't been properly operated, but the companies involved learn a painful lesson.
I note that you have a Banking Ombudsman service in Canada. https://www.obsi.ca
Our services are free to customers
MAKE A COMPLAINT
I must make it clear that you complain to your bank about the unauthorised charge to your account. If they don't reverse it, then you go to the Ombudsman but follow the steps they lay out. The bank allowed the charge. It's their responsibility. When you first mention that you want the charge reversed (be polite but firm) mention that you will refer it to the Ombudsman if it is not resolved.
Any other victims should do the same. A company that has been doing this a lot will find their facility and ability to originate account charges will go up in flames if faced with a lot of reversed charges.
Just to be certain - they didn't use your debit or credit card to charge you did they ? From what you say they didn't, but if they didn't and you didn't authorise a charge, instructing your bank to reverse it is the way to go.
Even if you did, it doesn't close your options, but just alters them. I mention this for others who may have been affected.