I am not a lawyer. So this is not legal advice, etc.

As the other responder said: ask them for the agreement you signed that said you’d pay a broker fee.

A verbal agreement won’t count - under contract law any such agreement would require “meeting of the minds” meaning you and the agent understood the same thing. You’re from out of town and had no idea what the broker fee meant so clearly you didn’t have an agreement.

If the agency didn’t have you sign an agreement I’m betting the person who showed you the properties is going to be in trouble with their boss. And that if you just ask them for the signed agreement where you agreed to the broker fee of one months rent they’ll shove off.

You may want to have a lawyer send their lawyer a letter though for emphasis.