You may be reading more into this that it might deserve. "Their synagogue" is simple the synagogue for the local Jews in the area. But then maybe not.
Apart from not being a Samaritan synagogue, I believe that it may be possible that Our Lord was referring to the Great Synagogue of Jerusalem that had ”the important rôle of forming the Canon of the Old Testament.”
From the outset of Christianity the synagogue was in full power of its various functions; the New Testament speaks thereof fifty-five times. The word is used to denote the body politic of the Jews twelve times: twice in Matthew (x, 17; xxiii, 34); once in Mark (13:9); three times in Luke's Gospel (viii, 41; xii, 11; xxi, 12), and four times in his Acts (vi, 9; ix, 2; xxii, 19; xxvi, 11); and twice in the Johannine writings (Revelation 2:9; 3:9). The more restricted meaning of meeting-house occurs forty-three times in the New Testament — seven in Matthew (iv, 23; vi, 2, 5; ix, 35; xii, 9; xiii, 54; xxiii, 6); seven times in Mark (1:21, 23, 29, 39; 3:1; 6:2; 12:39); twelve times in Luke's Gospel (iv, 15, 16, 20, 28, 33, 38, 44; vi, 6; vii, 5; xi, 43; xiii, 10; xx, 46), and fourteen times in his Acts (ix, 20; xiii, 5, 14, 42; xiv, 1; xv, 21; xvii, 1, 10, 17; xviii, 4, 7, 19, 26; xix, 8); twice in John (vi, 59; xviii, 20); once in James (ii, 2). Our Lord taught in the synagogues of Nazareth (Matthew 13:54; Mark 6:2; Luke 4:16), and Capharnaum (Mark 1:21; Luke 7:5; John 6:59). Saint Paul preached in the synagogues of Damascus (Acts 9:20), Salamina in Cyprus (Acts 13:5), Antioch in Pisidia (Acts 13:14), Iconium (xiv, 1), Philippi (xvi, 13), Thessalonica (xvii, 1), Boræa (xvii, 10), Athens (xvii, 17), Corinth (xviii, 4, 7), and Ephesus (xviii, 19). It is worthy of note that despite his frequent use of the Jewish meeting-house, St. Paul in his stern antagonism never once deigns to make mention of the synagogue. He designates Judaism by the term "circumcision", and not, as do the Evangelists, by the word "synagogue". And even in speaking of the Jews as "the circumcision", St. Paul avoids the received word peritomé, "a cutting around", a word employed by the Alexandrian Philo for Judaism and reserved by the Apostle for Christianity. The sworn foe of the "false circumcision" takes a current word katatomé, "a cutting down", and with the vigorous die of his fancy, stamps thereon an entirely new and exclusively Pauline meaning — the false circumcision of Judaism.
At the time of the destruction of Jerusalem (A.D. 70) there were in the city itself 394 synagogues, according to the Babylonian Talmud (Kethuth, 105a); 480, according to the Jerusalem Talmud (Megilla 73d). Besides these synagogues for the Palestinian Jews, each group of Hellenistic Jews in Jerusalem had its own synagogue — the Libertines, the Alexandrians, the Cyrenians, the Cilicians, etc. (Acts 6:9). Josephus speaks of the synagogue which Agrippa I erected in Dora (Antiq., XIX, vi, 3), of the Cæsarean synagogue which revolted against Rome (Bell. Jud., II, xiv, 4), of the great synagogue of Tiberias (Vita, 54), and of the synagogue of Antioch in Syria to which the sacred vessels were borne away in the time of the Seleucid War (Bell. Jud., VII, iii, 3). Philo is authority for the existence, during the first century A.D., of many synagogues in Alexandria (Leg. ad Gaium, 20), and of not a few in Rome (Ibid., 23). In Northern Galilee, are numerous ruins whose style of architecture and inscriptions are indications of synagogues of the second and, maybe, the first century A.D. The Franciscans are now engaged in the restoration of the ruined synagogue of Tel Hum, the site of ancient Capharnaum. This beautiful and colossal synagogue was probably the one in which Jesus taught (Luke 7:5). Of the ruined synagogues of Galilee, that of Kefr Bir'im is the most perfectly preserved. Various Greek inscriptions, recently discovered in Lower Egypt, tell of synagogues built there in the days of the Ptolemies. A marble slab, unearthed in 1902 some twelve miles from Alexandria, reads: "In honour of King Ptolemy and Queen Berenice, his sister and wife, and their children, the Jews (dedicate) this proseuché. Both the Jerusalem and the Babylonian Talmud make mention of numerous Galilean synagogues which were centres of rabbinical literary, and religious and political influence at Sepphoris, Tiberias, Scythopolis, etc. Every Jewish settlement was obliged by Talmudic law to have its synagogue; the members of the community could oblige one another to the building and maintaining thereof; indeed the members of the Jewish community were designated "sons of the synagogue". For further history of the synagogue, see JEWS AND JUDAISM.
The Great Synagogue is worthy of special mention, as to it is assigned, by Jewish tradition, the important rôle of forming the Canon of the Old Testament. It is said to have been founded by Esdras in the middle of the fifth century B.C., and to have been a permanent and legislative assemblage for two and a half centuries. The Mishnah (Pirke Aboth, I, 1) claims that the Prophets handed down the Torah to the men of the Great Synagogue. "Aboth Rabbi Nathan" (a post-Talmudic treatise) paraphrases this statement by including the last three Prophets in this assemblage: "Aggeus, Zacharias and Malachias received [the Torah] from the Prophets; and the men of the Great Synagogue received from Aggeus, Zacharias and Malachias". How long this supposedly authoritative body held control of the religion of Israel, it is impossible to tell. Jewish chronology from the Exile to Alexander's conquest is far from clear. Rabbi Jeremiah (Jerus. Talmud, Berakot, 4d) says that one hundred and twenty elders made dictions of Kiddush and habdalah. The Talmud, on the contrary (Peah, II, 6), hands down Torah from the Prophets to the Zugoth (Pairs) without the intervention of the Great Synagogue. Be the Great Synagogue of Jewish tradition what it may, historical criticism has ruled it out of court. Kuenen, in his epoch-making monograph "Over die Mannen der groote synagoge" (Amsterdam, 1876), shows that a single meeting came to be looked upon as a permanent institution. The Levites and people met once and only once, probably on the occasion of the covenant described by Nehemias (Nehemiah 8-10), and the important assemblage became the nucleus round which were wrapped the fables of later Jewish tradition. Such is the conclusion of W. R. Smith, "The Old Testament in the Jewish Church", p. 169; Ryle, "Canon of the Old Testament", p ú Buhl, "Canon and Text of the Old Testament", p. 33; Driver, "Introduction to the Literature of the Old Testament", 6th ed., p. 7.
Seeing that Jesus was in conversation with the Pharisees, it makes sense that he was referring to the Great Synagogue of Jerusalem.
It all seems to point to the Great Synagogue, for both the Pharisees and/or Scribes!
