Answer:
In an ATM interchange deposit environment, liability of an ATM deployer to a card issuing bank is addressed in the network contract or operations procedures. However, if Jane Smith in your hypothetical makes a claim of non-payment upon the issuer of the check, and the issuer of the check initiates a claim on the paying bank, which results in a presentment or transfer warranty claim against your bank as depositary bank, you'd be responsible for that claim, and you'd have to look to the network agreement for recovery from the card issuing bank.