To check your e-file status, someone would have to either log into your account, or have some very sensitive information. They would need your full Social Security Number and the exact amount of the refund you're expecting, plus your filing status (single, married filing jointly, etc.). The best way to make sure no one else can check your status is to make sure your account is secure. You may want to change your password, to be sure that you're the only one who has it.
