Nice to hear from you again.
The so-called "Grenzübertrittsbescheinigung" (GüB) is a document that you have to submit to officials when you are leaving Germany at Ausländerbehörde's disposition. These officials at the German border will then inform Ausländerbehörde that you left Germany. Otherwise Ausländerbehörde will start investigating where you are and arrest you if they find you.
Whether or not you are allowed to re-enter Germany depends on the circumstances why you had to leave. If you got deported after your asylum application got rejected, then you probably have an entry ban that is valid for a certain time. The exact validity period depends on your individual case.