You do not need a liquor license to be an employee of a licensed establishment. Background checks are only done on sole proprietors, general partners, or substantial owners of corporations/LLCs.
You're going to have to tell us just what sort of license you are applying for and why you think you need one?
Mostly they're going to want you to explain these, especially with regard to whether they had anything to do with alcohol. Other red flags are non payment of taxes (especial sales/excise etc...).