These relics are quest items.
In the original launch version of the game, quest items went into your inventory. Inventory full. You could not advance quests that required you to gather items. Delete a quest item out of your inventory, it would cancel the quest.
The newer implementation is for quest items to be stored in your quest log. If you open this quest right before you turn it in, you will see the relics attached to the quest.
Tier 4 relic too weak for you. Combine it with other tier 4s to get a tier 5. Combine the tier 5s to get a tier 6 - hopefully the relic that you want.
Unless stated otherwise, all content in this post is My Personal Opinion.