How come you are allowed to own money in Chutz la'Aretz since it has some Avodah Zarah on it?
I am unsure which Avodah Zarah you refer to. Perhaps the word "god" on US currency. However, there is no prohibition on owning a paper which has the name of an Avodah Zarah on it. The prohibition on owning Avodah Zarah or benefitting from Avodah Zarah involves either owning the actual article served, or the things that service the Avodah Zarah (Meshamshim) or things that are offered to the Avodah Zarah as sacrifices.