Do You Know What a Xenodochium Is?

I didn't.

But it is

a room (or separate guest-house) in a monastery religious building such as a synagogue or monastery for the temporary accommodation of guests or pilgrims

Now, from where did that come from?

From a book review that highlights the Jewish history of the city of Jerusalem during the

chronological spectrum [which] embraces nearly a millennium (c. 300 BCE to c. 640 CE), and the editors ought to be commended for attempting to break away from the traditional chronologies that have dominated the field of Jewish studies. Thus, instead of "Second Temple" and the "Mishnah" and "Talmud" eras (c. 450 BCE to 70 CE; c. 70 to c. 200 CE; and c. 200 to 400/600 CE, respectively), the editors have adopted the conventional classical boundaries of the "Hellenistic" period (which they do, however, terminate with the destruction of the Second Temple in 70 CE); the "Roman Period" (from 70 to Constantine), and "Late Antiquity" (from Constantine to the Arab Conquest).

And as for that inscription where that word, xenodochium appears:

Another inscription (no. 9), also in Greek, is a perennially problematic one, erected by Theodotos, and found south of the Temple Mount. It seems rather handsome by comparison with the scribbling nature of most of the Greek, Hebrew and Aramaic documented in this volume. The inscription records both the genealogy of Theodotos, son and grandson of archisynagogues, as well as the contribution of the family to the building of a synagogue complex which included even a xenodochium. If the synagogue operated "in the shadow of the Temple" (p. 55), then one wonders what, precisely, its functions were, in addition to offering hospitality to "those who are in need of it from abroad". That the synagogue itself is designated as a place "for the reading of the law (nomos) and the teaching of the commandments" seems to indicate that it served as a space of learning to read the Torah rather than of praying. Nor is it clear whether such synagogues thrived in competition or in collaboration with the Temple. Perhaps, as the editors propose in the wake of many others, the family of Theodotos had been transplants from Italy and were accordingly attuned to the needs of fellow immigrants and fellow pilgrims.

All of gthis, of course, is to counter Arab propaganda claims of (a) no Temple in Jerusalem; (b) no thriving Jewish national life in Eretz-Yisrael; and (c) the lack of Arabs in the area until they copnquered and occupied a country that wasn't there's.

^