The anime covers the encounter with the water spirit in episode nine of season one.
While asking the spirit about getting the ingredient (a part of her body), Montmorency informs Saito that the spirit is immortal, and so has a different perception of time. After later learning that she is seeking the ring of Andvari, Saito immediately promises to find and return the ring.
Guiche mocks him, saying a spirit won't trust some non-mage commoner it's never met. The spirit immediately agrees, saying that Gandalfr has kept his promises before, so he can be trusted. She hands over the ingredient in the same action.
At this stage they do not know what "Gandalfr" really is, but the mission is accomplished. When Montmorency questions him why he would so casually agree to it, saying how he'll find it one day, he points out that since the spirit is immortal it won't really mind if it takes years for him to complete the quest.
The ring remains unreturned in the novels. You can expect it to remain that way forevermore:
We regret to report that Zero no Tsukaima's creator has passed away from his long battle with cancer. May he find rest in Halkeginia.
Noboru Yamaguchi R.I.P