Banks are required to report cash deposits or deposited checks of more than $10,000.00 to the IRS.
There are records kept at the bank of checks deposited into checking or savings account however banks do not keep records of cashed checks and I've never had cashed checks show up on any IRS income audit or anything.
Also banks will usually only report money to the IRS if it's a big enough amount of money for them to be required too since reporting to the IRS is another time consuming job and if they're not required to report the money then they won't do so.