I suggest you write it, otherwise others will never know your work experience and don't want to continue to know it. After all, there are too many people looking for jobs. In fact, the background check is a very late step, at least you have to pass the interview and accept your will. Moreover, not all companies do background checks. Even if they do this, they must get your consent in advance. Generally, you should provide the contact information of the referrer, instead of calling your company and asking anyone about you. So don't worry, it's normal to find a job.