You can easily destroy Time Rifts by using Ecclesia Purification Cup.
Though Ecclesia Purification Cup is quite rare considering that it can only be obtained by a special event (e.g New Year Chest) at least we have another way in getting it by using the Adventurers Meatball.

Use Adventurers Meatballs and a new option will appear, it will let you choose which Ecclesia Purification Cup you want to purchase, This version of  Ecclesia Purification Cup can only be used in specific locations, unlike the one that is obtained in the event.

The process is still the same when doing the normal Time Rift, its just using Ecclesia Purification Cup makes it instant.
Go near a Time Rift with your Ecclesia Purification Cup and it will prompt if you want to use the Cup or do it in a normal way.

Click the Instant function and it will automatically Destroy the Time Rift with your loots.