You ask whether an agent of a corporation (e.g. a customer service representative) can accept on behalf of the corporation a contract offered to them that would have the corporation pay the offeror a fee for time spent on the phone call.
For the contract to be binding:
- the agent must have actual authority to enter into it on the corporation's behalf; or
- the agent must have apparent authority to enter into it on the corporation's behalf (the point made in Freeman and Lockyer, below), without this apparent authority being negated by the counterparty's knowledge or constructive knowledge that the agent lacked actual authority (the point made in Criterion Properties, below).
Unless they have actual authority, the person purportedly accepting the contract on behalf of the corporation would have to have the "apparent authority" (also called "ostensible authority") to bind the corporation.
For a contractor to be able to enforce a contract against a company, entered into by a customer-service representative (agent) with no actual authority to do,1 four conditions must be satisfied (Freeman and Lockyer v Buckhurst Park Properties (Mangal) Ltd  2 QB 480):
- that a representation that the agent had authority to enter on behalf of the company into a contract of the kind sought to be enforced was made to the contractor;
- that such representation was made by a person or persons who had "actual" authority to manage the business of the company either generally or in respect of those matters to which the contract relates;
- that he (the contractor) was induced by such representation to enter into the contract, that is, that he in fact relied upon it; and
- that under its memorandum or articles of association the company was not deprived of the capacity either to enter into a contract of the kind sought to be enforced or to delegate authority to enter into a contract of that kind to the agent.2
See also Criterion Properties Plc v. Stratford UK Properties LLC & Ors  UKHL 28, para. 31:
If a person dealing with an agent knows that the agent does not have actual authority to conclude the contract or transaction in question, the person cannot rely on apparent authority. Apparent authority can only be relied on by someone who does not know that the agent has no actual authority. And if a person dealing with an agent knows or has reason to believe that the contract or transaction is contrary to the commercial interests of the agent's principal, it is likely to be very difficult for the person to assert with any credibility that he believed the agent did have actual authority. Lack of such a belief would be fatal to a claim that the agent had apparent authority.
The criteria from Freeman and Lockyer continue to be relied upon in recent judgments: Trafalgar Multi Asset Trading Company Ltd v Hadley & Ors  EWHC 1184 (Ch); Carlton Vale Ltd v Gapper  UKUT 141 (LC).
This answer takes no position on whether the customer service representative in the question's scenario would be found to have actual or apparent authority — that analysis depends on facts that are not presented in the question.
1. For many tasks (adjusting a cell-phone contract, providing a refund, agreeing to provide store credit, etc.), the corporation would have given the customer service representative actual authority to bind the corporation, which totally side-steps the apparent-authority analysis. Just because the agent has actual authority to agree to some things does not imply that they have actual or apparent authority to agree to other things.
2. When dealing with a director, or where a director is the one who has represented that an agent has authority to bind the company, this fourth criteria is rendered irrelevant by s. 40 of the Companies Act 2006.