The pre-Skyward Sword Sheikah are my favorite element of the entire franchise, and the cleansing of them as characters is one of the things that turns me off of the newer games.
Allow me to get
especially nerdy with you lot here.
The Sheikah Eye remains one of my favorite symbols in the franchise, and it's not just because it looks cool. It's because it's one of the most well thought out icons in a fictional world I've ever seen.
The proto-Sheikah Eye makes its debut in AlttP, as the symbol of Agahnim. But there's a distinct difference between it and the eye symbol found in OoT. It lacks the tear.
Come OoT, Impa now wears the same symbol, but with a tear. It later appears on Sheik, who, like Agahnim, covers his face with robes. We learn Impa built Kakariko Village, and we later discover Kakariko is built on the remains of a torture dungeon, and sits right next door to the Shadow Temple. This is all intentional. Attentive players will be put off by Impa and especially Sheik, because of the intentional similarities drawn to the villain of the previous game.
But it turns out to be a meta twist. They're the good guys.
I'll come back to OoT in minute, but for now let's segue to Twilight Princess to get a clearer picture of the narrative. In TP, we learn of the Interlopers, a mysterious race of shadow people who, decades ago, attempted to take over Hyrule and steal the Triforce. The game never explicitly says the Interlopers are the Sheikah, but it hints at it at every opportunity. On the back of Zant's throne room, and the on the back of Midna's helmet, we can find the Agahnim version of the eye, sans tear.
The implication is abundantly clear. The Sheikah were not good people. They attempted to take the Triforce for themselves. They built underground torture dungeons and temples to the shadow gods. Most of them were banished to the Twilight Realm, while a select few stayed. Those select few swore fealty to the Hyrule Kingdom, and adorned their Eye with the Tear, a representation of guilt.
Back to OoT specifically. Bongo Bongo is the shadow god that the Sheikah followed. His giant eye is literally the Evil Eye symbol.
Those "spikes" around the Sheikah eye are in fact the strands of flesh coming off Bongo Bongo's decapitated neck.
The backstory of OoT talks about a recent war, where King Hyrule unified all the peoples of Hyrule to win the war. Notably absent from OoT is anybody for the peoples of Hyrule to
fight in this war. The idea that it was the Gerudo doesn't gel with the fact that Ganondorf's help in ending the war is what gets him close to the king in the first place.
The backstory of TP talks about the attack on the Sacred Realm by the Internlopers, and in AlttP, we learn that when word of the Triforce first spread, it caused a civil war where the people of Hyrule all fought to seize its power.
I believe all three of these events are the same thing.
So, just prior to OoT, the Sheikah, a race of dark, shadow people, learn of the Triforce's location in the Sacred Realm, and attempt to take it for themselves. They most likely use the Mask of Truth (notable again in that it features the tear-less Eye symbol) to learn how to gain access to the Sacred Realm. And they definitely use Bongo Bongo's power in their attempt to seize the Triforce.
They King of Hyrule, with the the help of Darunia, Zora and Ganondorf, fight back the attack of the Sheikah, and at some point, Impa turns on the other Sheikah and seals Bongo Bongo in the dungeon under Kakariko. This is enough to convince the King to spare her.
The Sheikah interlopers are defeated and sealed in the Twilight Realm for their crimes. Impa is spared, builds Kakariko Village for the Hylians as a show of good faith, and swears fealty to the King and is placed as the princess's bodyguard.
And to clearly denounce her old ways, she adorns the Evil Eye with the tear.