Just some observations of a general nature. I live in the UK but the same general legal principles apply.
Without an authority your bank has no legal right to charge your account with anything. You may be uneasy doing it, and you would be right to be cautious, but the harsh truth is that if the party originating the charge doesn't hold your legal authority to do so, your bank has to refund you. How they get the money back is up to them. Your bank is the guardian of your money and it is their responsibility as to whether or not the other party has legal authority to charge your account.
You, as an individual, can't go in to your bank and originate a charge to another account and normally only substantive companies can do so, but they're still obliged to ensure that they hold a proper authority. If they don't, and they're misusing the ability to originate charges, the facility will taken off them, but they will have signed an indemnity enabling funds taken in error to be recouped from them.
Knowing your account details DOES NOT give any right to charge your account. If you issue a cheque it gives details of your account and a specimen of your signature. In the UK a payday lender alleged it had account details submitted by fraudsters together with the birth dates of innocent victims and it issued hundreds, if not thousands, of charges with no legal authority to do so. The company was shut down and all payments were refunded.
You can form a legal contract online, and the steps and details as to the legal requirements and when the contact is actually formed is likely to differ from one country to another.
One thing that puzzles me is that no one mentions whether or not the original loans were ever received. If you never received the original loan, then it would appear self-evident that the charges are fraudulent.
I'm not a legal expert. I do not know Canadian law or the details of these particular circumstances, but if you've never received the loans to which these repayments supposedly relate, then I would feel inclined to repudiate the charges, and leave your bank with the problem.
This may interest youhttp://www.bbb.org/ottawa/business-reviews/loans/upper-canada-loans-in-ottawa-on-47097
In Ontario, it is illegal for a loan company to charge an advanced fee for a loan. All fees should be included in the borrowing cost of a loan.
Looking at the website it appears that they only offer to put you in contact with lenders and not arrange a loan themselves. The point will then be what they claim they were charging you for and whether, if it was an advance fee for a loan, it was a legal charge and whether you actually ever agreed to pay it.