I've commented to your question seeking some clarification. This answer is without that clarification.
There are two questions called in your OP: (1) would a phone call have been enough to terminate the original agreement? and (2) if the phone call terminated the agreement, are the terms of the Termination Notice valid and enforceable?. The short answer to both is that it depends on all of the relevant communications between your friend's business and the CC processing company (none of which is included in your post). But my best guess is (1) No; and (2) No, but since the answer to (1) was "No" this is irrelevant.
A binding contract at common law generally requires an offer, acceptance, consideration, and mutual intention to be bound. In this case, it is likely that the Application was an offer by your friend's company to do business with the CC processor on terms that they set out. Those terms may have been printed on the back of the Application, or hidden somewhere on their website, or someplace else entirely. When the CC processor agreed to do business with your friend's company, that was the acceptance. The consideration on the CC processor's side was the promise to facilitate CC payments, and on your friend's side was the fee deducted from each transaction. And the mutual intent to be bound was evidenced through the course of dealings of the parties. It is irrelevant whether the entire agreement between the parties was ever written down or signed: that would provide good evidence of the contract, but it is not the contract. The contract is just what the parties agreed to do. My best guess is that the CC processor had terms someplace that included contract termination provisions. Those provisions, in turn, had something like a minimum contract length, minimum earning provision, or a termination fee. That, and not the Termination Notice, is what gave rise to the requirement to have a written termination and the deduction of a fee from your friend's business account. If I am correct about those things, then the answer to your first question is "No": because the telephone call does not comply with the (potentially hidden) terms, it would not be sufficient to terminate the agreement.
But if there were no such terms, or if there were but they permitted oral termination of the agreement, then the Termination Notice was probably insufficient to authorize the payment. The reason for this is the Termination Notice was almost certainly not a contract. In particular, while your friend's company gave the CC processor consideration (the $$,) the CC processor did not give your friend anything in exchange under the Termination Notice. Terminating the agreement was not valid consideration: the telephone call had already done that. That means the payment was a gratuitous, and unintentional, gift. Such gifts are not enforceable, and your friend should be able to dispute the charge and get the money put back. But that's IF the telephone call terminated the relationship, and as I said above that IF is very, very unlikely.
The next question you might ask was whether something else, other than the telephone call, may have terminated the relationship. The answer there is, "maybe". In some jurisdictions, there are laws that protect consumers (even business consumers, like your friend's company) from lousy contracts, hidden terms, unfair and deceptive practices, and the like. Sometimes these protections make such agreements automatically invalid, particularly if the method of entering into them was also unfair. Other times the protections do not invalidate the contract itself, but provide for penalties against the ne'er-do-well that uses the bad tactics. Your best strategy may be to track down the Application, any agreement terms, etc. and gather facts about how the service was advertised, what promises or representations were made, and the mechanics of signing up for the service. Then talk to a local attorney about whether the agreements between the parties may have been "void" or "voidable," particularly for fraud, unconscionability, or violation of an applicable unfair trade practice or consumer protection statute. Also ask whether there may be some remedy sounding in equity or tort for sharp practices, or statutory remedies. If there are affirmative claims or defenses against the withdrawal, the best course is probably to have the attorney send a letter to the CC processor's registered agent explaining them and offering to settle.