In Pokémon Legends: Arceus, when the Griseous Core is used from the satchel on Giratina, it switches between its Altered and Origin Formes.
In Pokémon Scarlet and Violet, if a Giratina is holding a Griseous Core, it changes to its Origin Forme. Additionally, it boosts Giratina's Dragon- and Ghost-type moves by 20%.
The Griseous Core's effect was previously granted in Generation IV through VIII if Giratina was holding the Griseous Orb instead. As of Generation IX, the Griseous Orb only boosts the power of Giratina's Dragon- and Ghost-type moves by 20% when held, but no longer changes Giratina to its Origin Forme.