backbround check

Hi, I got an onsite interview last week and most likely I can get an offer. One question is that I found I put a wrong time between the ending day (month) of my previous job and the starting day (month) of my current job: about three month difference. Do I need to send an email to correct?
I used to ask a hiring manager before and he told me that the background check is just for criminal. Your reply is greatly appreciated.