In general, a written contract is deemed to reflect the agreement that the parties reached and the parol evidence rule prevents the introduction of extrinsic evidence (like your previous emails or, indeed, this question) that contradicts the plain meaning of the contract.
The rationale for this rule is that parties adopt and abandon many positions while negotiating a contract but that when an agreement is reached and reduced to writing then what they write is what the agreed. While this is technically a rebuttable presumption, in commercial agreements between businesses (which are presumed to know what they are doing), it is virtually an inviolate rule.
The agency is a business, they wrote the agreement. Absent some overwhelming evidence, what they wrote is what the agreed.
Now, they do have some decent evidence:
- your payment of the higher amount (which may not be conclusive - you may have paid that amount to secure the property while negotiations were ongoing),
- this question. The fact that you admit that this is not what you agreed is pretty damning to your position.
- your testimony. When they put you on the witness stand and ask you if this was the rent you agreed to you will have to say "no". Unless you perjure yourself - that's illegal and unethical but you do you.
Now, if you were to sign the agreement and send it back with a note saying "Thank you for the lower rent. It was unexpected but much appreciated. Should I withhold the overpayment of the first month from the second month or will you refund it?" it's quite likely that you could make the lower rent stick. They would be in no position to claim that you had known they had made a mistake (you genuinely thought they were being generous) and that you took advantage of it.