I cannot answer your question completely or accurately because it will greatly depend on the details of your case. Generally speaking, oral agreements may be enforceable contracts, except for those agreements that fall under the Statute of Frauds. To know if the Statute of Frauds applies to your particular case or if this particular agreement is binding, you need to speak with an attorney. Contract law is very fact specific and requires the attention of an attorney.
I would have them put it in writing. Did you ask them to send you a written confirmation?
The response is based on the information provided. Absent an express agreement, this communication does not constitute legal advice or create an attorney-client relationship.
More than likely, the agreement could be binding on you. That particular firm does a lot of collections and shoplifting cases. I suspect that they record all calls. If you don't pay according to your agreement, they may sue you. If you still intend on paying, but just want the payments to be less, call them and renegotiate. Or just send in a lesser amount. They will probably accept it as long as it keeps coming in every month.