Yeah, from looking at the archdiocese website, it says that they're members of a committee which sponsors a prayer service as part of a "Week of Prayer for Christian Unity", and is "a catalyst for ecumenical courtesy" (I guess that's like regular courtesy, but with heretics). I don't see any evidence from the website that they actually pray together, only that they sponsor this thing. You could say that's bad enough, I guess, but it is a difference.
Looking around further for general information, it seems that the "Week of Prayer for Christian Unity" was started c. 1930 by a Catholic priest, joined by Anglicans and later by other Protestants. Today it involves the World Council of Churches (which includes most EO churches, except for Georgia, Bulgaria, and Estonia), because that organization propagates preparatory materials for the week (since so many of its member churches that are Catholic or Protestant participate in it), but if you look on
their website (I know...it's creepy), you see that the materials for the observance of this week are available in English, French, German, Spanish, and Portuguese. That's it. No Greek, Russian, Arabic, etc. That's a pretty big clue as to who probably actually
participates in the week (or at least who disseminates information about the week in their own churches), versus who is just a member of another organization that happens to sponsor it due to other members' in the same organization being among those who participate in it.
So it seems like primarily a Catholic and Protestant thing which Eastern Orthodox jurisdictions are only at best tangentially related to.
