Alright, let's go to details:
http://www.heraldica.org/topics/orders/wom-kn.htm
(your link)
"It is the order of the Hatchet (orden de la Hacha) in Catalonia. It was founded in 1149 by Raymond Berenger, count of Barcelona, to honor the women who fought for the defense of the town of Tortosa against a Moor attack. The dames admitted to the order received many privileges, including exemption from all taxes, and took precedence over men in public assemblies. I presume the order died out with the original members. "
Likely "the order died out with the original members" ... so irrelevant.
The next:
"In Italy, the Order of the glorious Saint Mary, founded by Loderigo d'Andalo, a nobleman of Bologna in 1233, and approved by pope Alexander IV in 1261, was the first religious order of knighthood to grant the rank of militissa to women. This order was suppressed by Sixtus V in 1558."
That's founded and approved inside the crusader time ... there is a general break in the knight orders development with the fall of Akkon and the fall of the Templer. It seems likely, that the order was irrelevant in 14th century, cause Italy developed the Condottieri system and this seemed to contradict the knight orders ideas for some time. It seeme, that the knight orders idea was reimported to Italy possibly in the 1450's (Francesco Sforza and Jacopo Antonio Marcello were Italian "Knights" in the French order of Rene d'Anjou, likely becoming member in 1451 or 1452 in a specific political situation (pause of the war Milan-Venice) - actually this was not really a knight-order-game, but a diplomacy game (what knight orders often were).
Well, it's interesting: Filippo Visconti took control of Bologna (city of the order of the glorious Mary) during the council of Ferrara 1438.
Filippo - as above in other articles postulated - created the knights-as-court-cards-phenomenon in 1441, then still in possession of Bologna, and Filippo knew and was interested in the the story of Jeanne d'Arc. ... was it perhaps Filippo himself, who revived the old story of the order and reconstituted it?
Or happened the reconstitution in the general stream of a modern-way Knight order system, which spread in Italy in the 1470's, likely following French and outlandish influences?
A constant existence of the order seems very doubtful.
Sixtus V.
http://www.newadvent.org/cathen/14033a.htm
the one, who prohibited the order:
"Born at Grottamare near Montalto, 13 December, 1521; elected 24 April, 1585; crowned 1 May, 1585; died in the Quirinal, 27 August, 1590. He belonged to a Dalmatian family which in the middle of the preceding century had fled to Italy from the Turks who were devastating Illyria and threatened to invade Dalmatia. His father was a gardener and it is said of Felice that, when a boy, he was a swineherd. At the age of nine he came to the Minorite convent at Montalto, where his uncle, Fra Salvatore, was a friar. Here he became a novice at the age of twelve. He was educated at Montalto, Ferrara, and Bologna and was ordained at Siena in 1547. The talented young priest gained a high reputation as a preacher. At Rome, where in 1552 he preached the Lenten sermons in the Church of Santi Apostoli, his successful preaching gained for him the friendship of very influential men, such as Cardinal Carpi, the protector of his order; the Cardinals Caraffa and Ghislieri, both of whom became popes; St. Philip Neri and St. Ignatius. He was successively appointed rector of his convent at Siena in 1550, of San Lorenzo at Naples in 1553, and of the convent of the Frari at Venice in 1556. A year later Pius IV appointed him also counselor to the Inquisition at Venice. His zeal and severity in the capacity of inquisitor displeased the Venetian Government, which demanded and obtained his recall in 1560. Having returned to Rome he was made counsellor to the Holy Office, professor at the Sapienza, and general procurator and vicar Apostolic of his order. In 1565 Pius IV designated him to accompany to Spain Cardinal Buoncompagni (afterwards Gregory XIII), who was to investigate a charge of heresy against Archbishop Carranza of Toledo. From this time dates the antipathy between Peretti and Buoncompagni, which declared itself more openly during the latter's pontificate (1572-85). Upon his return to Rome in 1566 Pius V created him Bishop of Sant' Agata dei Goti in the Kingdom of Naples and later chose him as his confessor. On 17 May, 1570, the same pope created him cardinal-priest with the titular Church of S. Simeone, which he afterwards exchanged for that of S. Girolamo dei Schiavoni. In 1571 he was transferred to the See of Fermo. He was popularly known as the Cardinal di Montalto. During the pontificate of Gregory XIII he withdrew from public affairs, devoting himself to study and to the collection of works of art, as far as his scanty means permitted. During this time he edited the works of St. Ambrose (Rome, 1579-1585) and erected a villa (now Villa Massimi) on the Esquiline.
Gregory XIII died on 10 April 1585, and after a conclave of four days Peretti was elected pope by "adoration" on 24 April, 1585. He took the name Sixtus V in memory of Sixtus IV, who had also been a Minorite."
Which should clearly tell, that Sixtus V. wasn't pope in 1558, but ...
"A year later Pius IV appointed him also counselor to the Inquisition at Venice. His zeal and severity in the capacity of inquisitor displeased the Venetian Government, which demanded and obtained his recall in 1560."
... as an inquisitor - who soon stumbled about his own feet he could cause some stress on some minor and not very important social institutions like the "order of the glorious St. Mary" (which likely was simply one of many strokes against some women emancipation, not a central important act).
The next one:
"In England, ladies were appointed to the Garter almost from the start. In all, 68 ladies were appointed between 1358 and 1488, including all consorts. Though many were women of royal blood, or wives of knights of the Garter, some women were neither. They wore the garter on the left arm, and some are shown on their tombstones with this arrangement. "
Well, the Garter was English - with logical great differences from the ustoms from the continent) and from begin on it had an erotic-ironical component ("garter"; "honi soit, qui mal y pense" ...
The French world and English customs were hostile to each for 100 years; Milan definitely was more influenced from France than from England, logically we should assume, that there was NOT a major influence from this side.
Next (militaric orders)
"Several established military orders had women who were associated with them, beyond the simple provision of aid. The Teutonic order accepted consorores who assumed the habit of the order and lived under its rule; they undertook menial and hospitaller functions. Later, in the late 12th century, one sees convents dependent on military orders are formed. In the case of the Order of Saint-John (later Malta), they were soeurs hospitalières, and they were the counterparts of the frères prêtres or priest brothers, a quite distinct class from the knights. In England, Buckland was the site of a house of Hospitaller sisters from Henry II's reign to 1540. In Aragon, there were Hospitaller convents in Sigena, San Salvador de Isot, Grisén, Alguaire, headed each by a commendatrix. In France they are found in Beaulieu (near Cahors), Martel and Fieux. The only other military order to have convents by 1300 was the order of Santiago, which had admitted married members since its foundation in 1175. and soon women were admitted and organized into convents of the order (late 12th, early 13th c.). The convents were headed by a commendatrix (in Spanish: commendadora) or prioress. There were a total of six in the late 13th century: Santa Eufenia de Cozuelos in northern Castile, San Spiritu de Salamanca, Santos-o-Vello in Portugal, Destriana near Astorga, San Pedro de la Piedra near Lérida, San Vincente de Junqueres. The order of Calatrava also had a convent in San Felices de los Barrios. "
I see nothing, which points to a relevant influence in the given question (1441, region of Milan or possible influence via diplomatic connection).
Still Jeanne d'Arc seems to be the "relevant theme of the moment"
###
Well, there is master Ingold from 1432 (short after 1431), and he knows of a deck with Kings, Queens and maiden instead the usual three more or less militaric male figures, something what Ingold seems to attack as "wrong" (likely too much women as court cards).