It's always a good sign when (if you extend the passage quoted in OP) an author is quoting himself...excuse me, misquoting himself...from his fictional spy novel. Right then.

But to undo the fever-dream "Vatican Illuminati" shades on the story:

On December 15, 1948, an anonymous Christian from the Netherlands wrote and dispatched a chunky, formal legal petition to the new Supreme Court of Israel. He assumed that the Court was the direct/same as the Sanhedrin that his Gospels told him convicted Jesus, and argued that the modern nation-state court revisit the verdict. Of course, insidiously implicit in the petition is the condemnation of the first-century Jews for falsely convicting Jesus and playing a/the key role in his execution. You know, the notion that has undergirded two millennia of anti-Jewish violence.

Enunciated in 1948.

The petition drew international media attention, because of course it did. And so it wasn't just one weirdo with some legal knowledge. In one particularly prominent example, American theologian Josef Blinzler's 1959 book on the trial of Jesus blared that Israel should "recapitulate the trial of Jesus and reverse the monstrously wrong verdict which was proclaimed at the time."

Who was having none of this? Moshe Smoira, Chief Justice of the Court. And future father-in-law to one Haim Cohn, then-future Attorney General of Israel. (That's right, Cohn--whose name Thomas gets wrong--wouldn't be AG until 1950). In addition to also being a renowned jurist, and ending up on Israel's Supreme Court later in his life, Cohn was a legal scholar.

Inspired by/frustrated with the petition Smoira received, Cohn took up the challenge in scholarship. His book The Trial and Death of Jesus Christ historicizes the Gospel account of the Sanhedrin meeting in contemporary Jewish law and practice. (Ultimately, Cohn argues that the Jewish "trial" was a desperate, last-ditch attempt to convince Jesus to back down off his claims so the Romans would not execute someone who was, after all, one of their own.)

The Vatican indeed had centuries-old priorities on its mind with the formation of Israel--most prominently, making sure Christians could still go on pilgrimage to their holy sites. However, relitigating the crucifixion, as it were, appears best left to fiction.

But, I say having read some of the Google Books preview, preferably not Gordon's fiction.

This incident is not mentioned in Silvio Ferrari (1985)'s "The Vatican, Israel and the Jerusalem Question (1943-1984)" Middle East Journal 39 (2): 316-331. It is also not mentioned in the Adriano E. Ciani's 2011 PhD dissertation at The University of Western Ontario, The Vatican, American Catholics and the Struggle for Palestine, 1917-1958: A Study of Cold War Roman Catholic Transnationalism, or in several other articles that I had access to.

I don't have access to all the print books Ciani singles out as particularly important in his literature review. However, if there had been such an offer, it would presumably have been mentioned in the dissertation or one of the articles I saw. It was not. I think we can safely assume that there was not an offer, because it is not in keeping with the Vatican's foreign policy.

The Catholic Church was much more concerned with territory than theology, right from the start of Zionism, as Ciani's dissertation points out:

Jews might return to Palestine to establish sovereign control there and that the most sacred Holy Sites of Christianity, directly related to the life and death of Christ, might fall under their jurisdiction, was unthinkable to the popes of the nineteenth and early twentieth century. Theodor Herzl, the founder of modern Zionism, discovered this in 1904 when he was received by Pope Pius X in Rome. “The soil of Jerusalem,” the pope informed his guest, “is sacred to the life of Jesus Christ. As head of the Church, I cannot say otherwise. The Jews did not recognize Our Lord and thus we cannot recognize the Jewish people.”

The Vatican continued this opposition of Jewish sovereignty of Christian sites more formally as Zionism gained strength, for instance opposing the Balfour Declaration.

Through the whole period, the Church's priorities seem to be 1. fighting for an international area around Jerusalem and Bethlehem, 2. securing Church properties in the Holy Land, then, 3. and 4. much more distantly, Christian Arabs and issues like specific taxes for Catholic institutions. Christians in the region were generally in favor of a Palestinian state, but the Vatican withheld official support for the internationalization of Jerusalem and, after 1947, the creation of a Corpus Separatum. The Corpus Separatum in the 1947 allowed Catholic countries like Belgium, France, and the Philippines to support partition, Ferrari argues.

You can see this in the public statements of the Vatican. They released several encyclicals in this period specifically about holy sites. Auspicia Quaedam (May 1948), In Multiplicibus Curis (Oct 1948), Redemptoris Nostri Cruciatus (April 1949). These were in fact the only encyclicals that Pius XII released in 1948 and 1949, to give some sense of the importance the Vatican gave these issues. If you read the encyclicals, the issues have nothing to do with a "new trial" for Jesus.

You can see Vatican policy somewhat in flux during this period as facts on the ground changed rapidly during the fighting in the civil war following the UN resolution, but the emphasis is the same. Auspicia Quaedam uses general languages and hopes "that the situation in Palestine may at long last be settled justly and thereby concord and peace be also happily established" while In Multiplicibus Curis explicitly says "it would be opportune to give Jerusalem and its outskirts, where are found so many and such precious memories of the life and death of the Savior, an international character which, in the present circumstances, seems to offer a better guarantee for the protection of the sanctuaries" and Redemptoris Nostri Cruciatus reiterates this desire in more detail.

The Vatican pushed behind the scenes for an international Jerusalem as well. For instance, Uri Bialy quotes a Knesset Foreign Affairs committee meeting from 1949 discussing meeting with the Brazilian foreign minister:

At the end of the talk, the minister said [...] that Brazil would vote the internationalization of Jerusalem, "because we must follow the instruction of the Vatican." Our representative asked: "Why must Brazil, which exerts such tremendous influence in this part of the world and is the leader of these nations, follow Vatican instructions on an issue in which it is not involved?" The Brazilian foreign minister replied that they were indeed involved. Brazil is a vast country, but precisely because it is so large, everything is fragmentary and the only two factors that unite the country are the army and the the [C]hurch. Every government in Brazil, water its standing and political orientation, must reinforce these two factors. Brazil has asked the Vatican to appoint a third cardinal, in addition to the two incumbents, for the north of the country for the purposes of internal cohesion, and they are now awaiting the Vatican's reply.

Ben-Gurion cited Catholicism as the third factor that led to Israel's defeat at the UN, after Russia and the Arab World. He said

"They mobilized about third mobilized about thirty countries, and it is evident that it was only the Vatican that brought pressure to bear, because some countries altered their stand overnight. Mexico, for example, abstained on the first vote but changed its mind at the Assembly ... The [South] American states are developed countries but have no desire to quarrel with Catholic power on our behalf.

Again and again, what we see is that the Church was intensely concerned about territory rather than theology. As a fun side note, the Protestant churches' responses were different, in no small part to the fact that Protestant churches have a much weaker tradition of venerating space and therefore much more limited tradition of either owning property in or encouraging pilgrimage to the Holy Land. John S. Conway's "The Founding of the State of Israel and the Responses of the Christian Churches" (1999) says "The Christian Century [an hugely influential American Protestant magazine], whose stance was both anti-Papal and anti-Zionist, regarded the whole idea of 'internationalization' as a Papist plot designed to turn Jerusalem and Bethlehem over to the Pope." Protestant sympathies were generally divided: some had strong ties to increasingly Protestant Middle Eastern Christian communities and were sympathetic to the Arab side, some (including Reinhold Niehbuhr), especially in light of the Holocaust, supported increased Jewish immigration and a Jewish state.

Gideon's Spies is not a reliable source. I generally don't rely on Daniel Pipes, but I think his review of the book gives you a sense of how it was received:

The book certainly contains many eye-popping claims. Thomas holds Israel's intelligence agency, the Mossad, responsible for the deaths of Princess Diana (whose driver it supposedly pressured to the breaking point); the publishing tycoon Robert Maxwell (whom it supposedly murdered); 241 U.S. Marines in Lebanon in 1983 (about whose planned fate at the hands of Hezbollah it supposedly had advance knowledge); and William Buckley, a CIA agent (whom it supposedly let die so the PLO would take the blame). Thomas's "secret history" also reveals that the Mossad helped the (failed) putsch of Soviet hardliners against Mikhail Gorbachev in 1991, and purposely destroyed the CIA's network in South Africa.

[...]There is much more in Gideon's Spies along the same or similar lines. It is, of course, impossible to confirm or disconfirm so-called findings based on secret tape-recordings or miracle computer programs manufactured by corporations obscure except to conspiracy theorists. […]

In any case, when it comes not to unverifiable assertions but to known and checkable facts, Thomas can hardly be said to inspire confidence. A few examples must suffice.

Thomas's command of Middle East realities is faulty in the extreme. He makes up Arabic words (no dictionary of mine has the word mafafeth, which he mistakenly believes means a meeting house) and mistranslates others (abu, or father, as "voice" being only the most egregious instance). He also routinely garbles common names, referring to Lebanon's Maronite Catholics as Marionites, to the Iranian arms dealer Ghorbanifar as Thorbanifar, and to Saddam Hussein's brother Sab'awi as Sabba'a. Chronology poses a particular stumbling block: Thomas misdates the Mossad's earliest roots by decades, has Richard Helms filling the position of director of Central Intelligence in 1957 (he actually took over in 1966), and calls the Yom Kippur war of 1973 the "second full-scale Arab war" with Israel, somehow forgetting 1967. And so forth.

And so forth indeed. As the Specator puts it, the author "has drawn on a mixed group of fantasists with claims to inside knowledge some of which hardly bear examination. From these sources, he has obtained a lot of tall stories, but little else that is not already in the public domain." No one else mentions this alleged incident and it seems to have little to do with what everyone seems to agree was the Vatican's policy priority in this period: securing a the safety of Holy places generally and internationalizing Jerusalem under a "third power" (neither Arab nor Jewish) more specifically. This offer would be strongly out of character for Vatican policy in the region in the 1945-1967 period, which was much more concerned with contemporary geography than ancient jurisprudence. (In 1967, the Pope called for a "special status, internationally guaranteed" rather than "international control" for Jerusalem, and formal relations between the Vatican and Israel began only in 1994). This policy was well-developed before Israel's Declaration of Independence in May 1948, and it is inconceivable to me that the Vatican would change it over something that goes completely unmentioned in the sources.