Here, the old woman will speak with you and Groose for a bit longer, mentioning that, to activate the Gate of Time, you need to hit it with a Skyward Strike. However, the sword you wield is far too weak for such. You are to go to the three main regions of the planet’s surface and purify your Goddess Sword in three sacred flames to power up your sword three times. Only then will you be able to utilize the Gate of Time.
After this, the old woman will suggest going back to Skyloft to learn the lyrics to the Ballad of the Goddess; they, in a sense, tell the prophecy of you. Afterwards, exit the temple (eastern door).
Go along the path back to Gorko. You’ll be shown a group of Blessed Butterflies. As mentioned earlier, you can play the Goddess Harp in front of certain groups of these insects to receive Gossip Stones or Goddess Walls; this group reveals the former.
These Gossip Stones will come up with a nice ol’ “Boing-oing”, dropping out a random treasure as well. You can hit them with your sword or a Bomb for somewhat humorous effects, and speak with them for advice and hints, some quite valuable.
Finish any other business you have here, then use a Bird Statue to return to the sky. Return to Skyloft, unless you’re going to do some Goddess Cube chest hunting.