Focus of background check for employers?

I just accepted a verbal offer from a great company. As per usual the official (written) offer is contingent upon passing a background check. There is nothing even remotely compromising on my record, so from that perspective I'm not worried about a thing.

However, I was very recently (and amicably) let go from a job after one month. I was given advice by a recruiter not to acknowledge it being that it was so short. Because of that I created a white lie to explain the small gap.

Will the above job show up on the background check, and could this be flagged as an issue by the prospective new employer? I'm just a little paranoid now about anything that could jeopardize my offer. I've never had to deal with a situation like this, so I would appreciate any advice or guidance. Thank you!

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