Did you read the billboard near the entrance of the temple complex? Click on it several times to cycle through the available postings. You can also ask about the ranking system in the nearby building, but I think you just need to read the message board to get the quest to recover a lost relic.
While the game can occasionally have a problem recognizing you have something if you find a quest item before getting the relevant quest, generally just dropping the item on the ground and picking it up again should be enough to get it working properly.
