The name might derive form the city of Granada in Spain, but the documented origin of this woven fabric is probably in Italy, there the main weaver are in or near Como in the North; there it is called Garza a giro inglese. It comes as large gauze garza grossa, fine or large gauze garza fina, and very small gauze garza piccola. Grenadine is less elegant that a smooth silk tie, but less casual that a knitted silk tie.
http://journal.styleforum.net/grenadine-fabric-history-tradition-and-ties/ Accessed 4 November 2019. (Blog with advertisements related to its content).
https://www.bondsuits.com/the-grenadine-tie/ Accessed 4 November 2019. (Blog with advertisements related to its content).
https://www.gentlemansgazette.com/all-about-grenadine/ Accessed 4 November 2019. (Advertorial).
Grenadine ties are silk-woven, such to give them more texture that classic silk ties. This is bespoke garza grossa Grenadine nectie from Sam Hober, who moved his tie-making business from the USA to Thailand. The delicate weave of the Grenadine fabric is typical for this type of necktie, which gives is a more structured feel and is the perfect accompaniment for a Friday suit. This six-fold tie was a bespoke order in 2009; the delivery was about 12 weeks later the order was confirmed.
Reference: I owe the lead to Sam Hober to Will Boehlke's website asuitablewardrobe.com, whose blog, as the new owners of the site announced, will be republished.