This article contains information that is considered canon in the "Steven Universe" universe.
"Homeworld Gems" is a term used by the cast, crew, and viewers to refer to the known, non-corrupted Gems who are or have been affiliated with the Gem Homeworld and are not members of the Crystal Gems. They are led by The Great Diamond Authority.
One of the Diamonds at the top of the Gem caste system. She is the supervisor and superior of Jasper and formerly Peridot.
One of the Diamonds. There isn't that much information about Blue Diamond, although she does appears to be a high-ranking authority figure, thus being a part of The Great Diamond Authority. Sapphire was a former member of her court.
A Quartz warrior assigned to escort Peridot on her mission to Earth who participated in the first war for Earth. Currently on Earth.
A Pearl who serves Blue Diamond. This Pearl seems to very calm and somewhat apprehensive to her owner. Blue Diamond's Pearl also acts mostly indifferent to her surroundings. She is rather opposite of Yellow Pearl.
A Pearl who serves Yellow Diamond. She is arrogant and somewhat sassy, though she is only fearful of her master Yellow Diamond.
Over 5,750 years ago, the Homeworld Gems arrived on Earth using the Gem Colony Ships and soon after, they built the Warp Pads for faster and easier traveling. During the time they had on Earth, they planned to terraform and colonize the planet, creating Kindergarten in order to produce more Gems at the cost of depleting the Earth of its resources which would inevitably cause great harm to the planet and its inhabitants.Feeling compassion and seeing the error in their ways, Rose Quartz rebelled and formed the Crystal Gems, a team of rebels who also wanted to protect the earth, and they started the war for Earth known as The Rebellion. Both sides fought valiantly against each other, but the battle that took place on the Gem Battlefield, the Crystal Gems finally won the war, which drove the remaining Homeworld Gems to retreat back to Homeworld, including Jasper. Many Gems were destroyed, reducing the original group of Crystal Gems (who originated on Homeworld) to Rose Quartz, Garnet, and Pearl.
The first member of the Homeworld Gems to be seen many years after the war was Lapis Lazuli, who had been trapped for thousands of years inside a mirror before Steven freed her. He healed her and she returned to Homeworld, only to regret it soon after as Homeworld had advanced so much in the time that she was trapped in the mirror and had found herself out of place. She was soon captured and forced to be the informant in the mission to check the Cluster along with a team of Homeworld Gems.
The second member of the Homeworld Gems to be seen was Peridot, who repaired the Homeworld warp at the Galaxy Warp. She was to check on the current status of the Cluster, but left after finding a Crying Breakfast Friends! sticker, which made her think the site was compromised.
She returned in "Marble Madness", where she tried to check on the Kindergarten again before Steven distracted her, which prompted her to attempt to kill him. However, the remaining Crystal Gems intervened and destroyed the main power source of the Prime Kindergarten Control Room, which made Peridot tell them that she would report what had happened.
Lapis was seen again in "The Message", this time using a Wailing Stone in Homeworld to send a message to Steven and the Crystal Gems of an approaching threat coming to Earth. Unbeknownst to them that Lapis had been forced to be the informant of the threat.
During the events of "The Return", Peridot brought with her two Homeworld Gems: her escort Jasper, and her informant Lapis Lazuli, traveling to Earth on the Gem Warship. Jasper helped Peridot defeat the Crystal Gems and take them back to the Homeworld. However, their plans were foiled when the Crystal Gems managed to fight back and defeat them, crashing their Warship in the process and stranding Peridot somewhere on Earth after she escaped on an escape pod. In one last ditch effort to defeat them, Jasper fused with Lapis to become Malachite, a monstrous fusion who sealed herself in the ocean by Lapis' will.
Peridot's primary mission for coming to Earth was seen in "Keeping it Together". She had, on various occasions throughout her appearances, been shown to be checking up on something called "the Cluster". In the aforementioned episode, the Cluster is revealed to be the result of fusion experiments done by the Homeworld Gems. The Homeworld Gems had taken the shards of fallen Crystal Gems from the war and experimented on them, forcibly fusing the shards to create it.