Consider asking the Bank Manager (or Assistant Manager) to verify that the role as described by the employment agency is true. That way they won't need to write their own letter, which may be against policy, but you can address CIC's concern. It also won't be perceived as simply insistent by the bank manager.
In this case, I would simply write a note to the bank manager explaining that you realize bank policy is not to write employment letters for people who work through employment agencies and explaining that CIC has requested additional information (first two paragraphs of GinnyPi's letter). Go on to explain that you received a letter from the employment agency which you submitted to CIC but CIC advised you that "You submitted a confirmation of employment issued by xyz employment agency describing your duties and conditions of employment with the bank as an Accounting Technician. I have concerns regarding your duties and responsibilities as an Accounting Technician because this information is not supported by evidence from the Bank of Montreal, for which you performed these duties." Therefore, you were hoping she could review it and verify that it does represent the role you actually performed at the bank or advise who could do so. Perhaps mention you'd greatly appreciate if she could jot a quick note down on the margin of the letter. This way she'll more likely need to reply either saying she can or explaining that it's also something she cannot do and you can either send the validated letter to CIC or send her reply explaining that she cannot help you due to bank policy and you can forward that to CIC to show that you've tried and that the bank doesn't disagree with the role but just doesn't offer letters in these cases or other means for you to validate the duties.
Good luck!
In this case, I would simply write a note to the bank manager explaining that you realize bank policy is not to write employment letters for people who work through employment agencies and explaining that CIC has requested additional information (first two paragraphs of GinnyPi's letter). Go on to explain that you received a letter from the employment agency which you submitted to CIC but CIC advised you that "You submitted a confirmation of employment issued by xyz employment agency describing your duties and conditions of employment with the bank as an Accounting Technician. I have concerns regarding your duties and responsibilities as an Accounting Technician because this information is not supported by evidence from the Bank of Montreal, for which you performed these duties." Therefore, you were hoping she could review it and verify that it does represent the role you actually performed at the bank or advise who could do so. Perhaps mention you'd greatly appreciate if she could jot a quick note down on the margin of the letter. This way she'll more likely need to reply either saying she can or explaining that it's also something she cannot do and you can either send the validated letter to CIC or send her reply explaining that she cannot help you due to bank policy and you can forward that to CIC to show that you've tried and that the bank doesn't disagree with the role but just doesn't offer letters in these cases or other means for you to validate the duties.
Good luck!