Background Check Question - Employment Dates

I had an on-campus job that I listed on my resume to have ended 1-2 months after the actual end date. This was an honest mistake because the school tried to place me into another position so I did not “officially exit” from the systems/payroll until 1-2 months after I had left the on-campus job. But in my background check, I put down the end date to be the date that my employer told me that they were going to transfer me to another position.

So now I’ve heard from the background check people to explain why there was this gap. I explained to them what I said above. I also have some records to prove this as it’s pretty ambiguous when my exact “end date” was. Is there anything that would happen to the background check?

Tl;Dr: On my resume I put the end date was 1-2 months after when I actually “stopped” working for an on-campus job, because of the extensive “transitional” period following the job. But on my background check I put in the actual date that I stopped working. Am I screwed...?