They should not. Its your personal matter with bank. The letter which company gave you has this line that this letter is issued on employee request with no financial obligation on company.

The only promise company made to bank is to keep transferring your salary to bank and to transfer your EOS to bank. You are not asking them to violate any of this so why do they want bank clearance letter?

They only need it if you are asking them to transfer your salary to an other bank.