It’s common to receive a mail from some service that they’re changing the terms and conditions of their service (internet provider, gmail, etc.) These changes are unilateral and can be about anything, from their privacy policy to the money they intend to charge me.
Why can’t I unilaterally send them a mail and say, I am changing the terms of my patronage and will now insert my new policy (pay only xx amount, or demand a mint Chico chip ice cream every Tuesday)?


IANAL. If a bank signs the copy they receive back from the counterparty, then generally yeah, it would be enforceable. Contract law demands that result, because otherwise there’d be no point to the words on the document. Working in the other party’s favor would be any lack of notice shortly after the bank signs the contract, because the longer the bank takes to notice a problem, the easiest it is to prove that they did not exercise the appropriate care when signing, incurring all consequences as a result. Missing more and more opportunities to recast or renegotiate the contract, that’s a poor position to defend.
That said, the other party must not have made any implied or explicit statements that the bank could have relied upon. Returning the modified contract to the bank in an email with the words “please find the signed contract attached” (my emphasis) could ambiguously imply that the original contract has been unmodified except that it has gained the other party’s signature.
Whereas the words “please find my signed proposal attached” would dispell any and all ambiguity, because it would clearly be a proposed contract by the other party, not the bank’s original proposal. Alternatively, a blank email with just the attachment is no statement at all, implied or explicit.
To be clear, a bank would almost certainly contest the contract, even if they don’t have a leg to stand on. And the usual reason for this – besides litigiousness – is that it’s the only way for the bank’s business insurance to pay out. Or at the very least, an attempt to slightly lower the damages by opening settlement talks.