She was an official ambassador. However, when a diplomat is accused of a major crime, like murder, the home country usually either waives the diplomatic immunity they granted their diplomat or charges them with the same crime on home soil, rather than risk an international incident. Examples of the former include Gueorgui Makharadze, and examples of the latter include Andrei Knyazev.

I think that's what happened to Wonder Woman.

Also, Themyscira did have an embassy, although it was closed down along with the island itself. You should read Rucka's run on Wonder Woman; there was a decent amount of focus on the people in the embassy, including a minotaur chef.