Will I lose my job offer?

• td insurance

I've been offered a job today at an insurance company and they're going to do a background check. I'm 18 and just finished being a student but I've put the date that I finished working part time at mcdonalds as the date of my last payment from them, when in fact I don't know the date I left anymore. I thought that was the best date to put down but I'm worried they'll think I purposefully lied. What should I do? Should I email them explains why the date might be different? Because the date I left is probably two or so months before what I've put on my cv, but I didn't do this to be deceitful. Please help.

Will I lose my job offer?