My two cents (in brief):
1) 'Establishing the social system' = salaat. 'Establishing the Quranic economic order' = zakaat. So the Quranic system is comprised of these two elements.
2) Since Islam is a system, not a religion, 'Muslim' refers to someone who 'submits' to the system. In the beginning, he/she swears allegiance to it, and 'belief' (eiman, status of a momin) comes later (49:14). The treaty/covenant was a basic constitutional agreement between peoples of various faiths to live under Islamic law socially and economically.
3) All parties had originally agreed to join/submit to the system. Later some parties attempted to rebel against the system, i.e. politically (salaat) and economically (zakaat). This was the equivalent of setting up a rival authority against Allah (hence, "idolators"). They were guilty of high treason.
4) This led to a declaration of war against those rebels - hence the opening line of surah tauba:
"Disavowal by God and His Apostle [is herewith announced] unto the idolators ..." (9:1) (I quote Asad only for the literal translation here)
Finally, to answer your question: "What are these Mushrikeen asked to come back/revert/repent to?"
5) "But if they repent, and establish salaat and zakaat..." (9:11)
In other words, The idolators (rebels) were given the chance to give up their campaign against the system. They were supposed to give and submit (and become "Muslim" again - that is, 'revert' to Islam).