The Meijer application form states that the company does a background check. Generally, most companies do background checks. However, the degree of its seriousness differs. For instance, Meijer’s background check, especially for entry-level positions, might simply be to determine whether you’re of legal age.
Therefore, you likely don’t have much to fear concerning background checks. Nonetheless, you should inform your hiring manager of anything serious during your interview. It’s preferable to play on the safe side and be honest right from the start.