Because of the nature of our business, we will ask to conduct a complete background check before hiring you at Marriott. Are there any issues that might hinder you from doing so?

Almost every hotel company will run a background check to weed out unhirable candidates. The interviewer is asking this question to screen you should there be an issue. This is the best time to be forthright and honest about any issue you might have, like a criminal record. Full disclosure may not make you exempt from employment with Marriott - they may need to understand the charge and assess the risk.