@Mami So I got curious and tried to practice some quick Google Fu. According to the Type Moon wiki, Gray appears in 3 places: Fate Labyrinth, Fate Strange Fake and here in Lord El Melloi II Case Files.
Of the 3 Fate Labyrinth is apparently a companion piece to Fate Fragments of a Silver Sky, a radio drama released starting in October 2017. This manga, Lord El Melloi II, began serialization in October 2017 as well. Fate Strange Fake seemingly originally started in 2008 from a joke before being published as a full on novel in January 2015 (announced 2014). In the 2015 novel, a woman calling Lord El Melloi II "master" has a passing appearance in a scene and is suspected to be Gray in the Type Moon Wiki.
Coincidentally, FGO was released late July 2015 for Android. So which comes first... Gray? Or the concept of the Saber/Artoriaface? It's hard to say that Gray was a fully developed concept by the time of her first potential mention. At the same time, I'm not quite sure when Saberface became the same thing. We could posit that perhaps they developed in step with each other. More Saberfaces for FGO meant more Arthur-related stories? Or perhaps the fomenting idea for Gray opening the way for rampant Saberface in FGO?
As a counterpoint, I think the idea of Saberface was beginning before FGO released. Acclaimed Saberface Nero first popped up in Fate Extra released July 2011. Then another Saberface we have is Jeanne d'Arc, who appeared in Fate Apocrypha first released December 2012. However, each of their designs in their original media might have differed until FGO. I don't know because I haven't consumed any of those works for comparison.
Is her background important to the plot? Sure, I won't dispute that, especially when I haven't read ahead. However, this does not dispute my claim of why more Artoria? We have Artoria basic, Artoria moody, young Artoria, Artoria on a horse, sexy Artoria on a horse, bikini Artoria, Japanese Artoria, Roman Artoria, Saintess Artoria... and now we have descendant Artoria. At least Japanese, Roman, and Saintess Artoria have unrelated backstories.
TL;DR: Ok maybe its important. IDK. But doesn't seem like Gray has been around longer than FGO.