Internship Background Check Help pls

Hello, 

I am scheduled to start an internship at a bank in a few months, and they started the employment background check process done by a 3rd party. I'm currently at another internship and lied to the bank I will be joining about the dates of my current internship as the two would overlap. Basically, I plan on leaving my current internship a little early to join the bank in question as I couldn't move back the start date. 

The problem is that as part of the background check they are asking me to provide the contract of my current internship, which will show that the dates of my current internship overlap with theirs. Should I just edit the dates on my current contract to fit the dates I plan on quitting and call it a day? How illegal is that, or should I just be upfront and tell them I plan on quitting my current internship a little early and send them the contract as it is? 

Thank you!