Any company entrusted with sensitive client information needs to exercise professional caution and safety checks when considering bringing on a new hire. Your best approach to this question is to express your willingness to comply with any form of background check they require. Exhibit professional transparency by sharing anything that might come up and providing context.
Background checks are costly, and it speaks to your professionalism by being conscientious about this. Not being transparent would suggest you're hoping issues from your past won't come up, which speaks to a lack of integrity and disrespect for their resources and time. If you're not sure if something from your past would appear on a background check, research everything and anything that might, and see if any of those apply to you.
