Did the myth of the holy grail originate from Catholicism?

The answer is no, the legend of the Grail does not source to Catholicism. According to NewAdvent.org who offers the Catholic Encyclopedia, the Catholic Church basically ignored the legend of the grail.

A word as to the attitude of the [Roman Catholic] Church towards the legend. It would seem that a legend so distinctively Christian would find favour with the Church. Yet this was not the case. Excepting Helinandus, clerical writers do not mention the Grail, and the Church ignored the legend completely. After all, the legend contained the elements of which the Church could not approve. Its sources are in apocryphal, not in canonical, scripture, and the claims of sanctity made for the Grail were refuted by their very extravagance. Moreover, the legend claimed for the Church in Britain an origin well nigh as illustrious as that of the Church of Rome, and independent of Rome. It was thus calculated to encourage and to foster any separatist tendencies that might exist in Britain. As we have seen, the whole tradition concerning the Grail is of late origin and on many points at variance with historical truth.

I highlighted a couple of lines about which comments must be made. First as to its point about a possible source, since when does the Catholic Church reject beliefs simply because it is not in Scripture? It doesn't. The real reason the Catholic Church supposedly ignored the Grail was because if true, its origins would place England as equal to, if not above, Rome, and certainly independent of her. Don't go searching for something that, if found, harms your credibility.

If one knows the history of the Easter controversy, one could probably understand this more deeply. So, long before Rome arrived, which NewAdvent is giving a nod to, Christians had arrived who observed Pascha (Easter like) on the 14th of the moon. When Rome finally arrived later, there was controversy over this because Rome observed the Sunday following the full moon following the Spring Equinox.

PS. The Valencia Chalice is not the Grail.

Although the Grail folklore seems to stem from the same centuries as the crusades due to Arthurian legends. Here is a little insight to its' origins. The origins are a mix of cultures. The medieval Church took no official stance on Grail folklore.

The Roots of the Holy Grail

Academic consensus gives the Grail a Celtic origin. The foremost campaigner for this view is Arthurian scholar Roger Sherman Loomis, whose book, The Grail: From Celtic Symbol to Christian Myth (1963), traces it to Irish tales of cauldrons and drinking horns that never run empty as well as accounts of journeys to the Happy Otherworld. The maiden Grail-bearer is based on the personified Sovereignty of Ireland, a woman who gives her cup only to the worthy. These elements were transmitted to Wales, then to Brittany, with Breton storytellers spreading them around northern France where the medieval romances first appeared. Loomis assumes that the material had been much altered by misunderstandings and oral process: There was no one "original" Grail myth.

But it was the connection with the Holy Eucharist that fixed the Grail in medieval minds. The old myths might never have gained such popularity without the Christianization that brought them in line with medieval iconography and devotional practice.

Grail romances appeared just as Eucharistic devotion was gaining favor, expressed in the elevation of the Host during Mass, Corpus Christi processions, preachers' parables, and miracle stories. Hosts that levitate, bleed, discriminate among recipients, serve as the sole food of saints, and reveal visions of Christ appear often in Eucharistic miracles and in Grail adventures. Devout contemplation of the elevated or exposed Host was believed to convey not only grace but well-being and protection, as does an encounter with the Grail.

The medieval Church took no official position on Grail romances. But the cathedral of Valencia claims to possess the actual vessel, a red stone cup from the time of Christ mounted as a splendid chalice during the Middle Ages. Its legend — which owes nothing whatever to the romances — claims that it was sent to Spain by the Roman martyr St. Lawrence. Donated to the cathedral in 1437, it's kept in a special chapel and was once used for Mass by Pope John Paul II. - The Real History of the Holy Grail

Valencia Chalice

Pope John Paul II himself celebrated Mass with the Holy Chalice in Valencia in November 1982. In 2006 at Valencia, Pope Benedict XVI also celebrated with the Holy Chalice, on this occasion saying “this most famous chalice”, words in the Roman Canon said to have been used for the first popes until 4th century in Rome, and supporting in this way the tradition of the Holy Chalice of Valencia. - The Holy Chalice of Valencia: Is it the Holy Grail?