As a warlock, you can only pick up one of these quests. Not both. So once you pick up one, the other should not still appear on the map.

https://www.wowhead.com/wotlk/quest=4963/shard-of-an-infernal

https://www.wowhead.com/wotlk/quest=4962/shard-of-a-felhound

Do you remember if you took the screenshot right after accepting "Shard of an Infernal" or at some point later? My Warlock does not see this quest up.

I completed one, but I can still see the other in Questie. But I can't pick it up -- it's not really there.

Both quests (4962 + 4963) are marked as exclusive to each other in our database and on top of that they both have 1799 marked as their next quest in the chain. So if either the other Shard of X quest or 1799 is in your quest log or complete (as you showed above) Questie should no longer show this quest 🙈

Can you do me a favor and run a few commands for me?

/dump QuestieLoader:ImportModule("QuestieDB"):GetQuest(4962).exclusiveTo
/dump QuestieLoader:ImportModule("QuestieDB"):GetQuest(4962).nextQuestInChain
/dump QuestieLoader:ImportModule("QuestieDB"):GetQuest(4963).exclusiveTo
/dump QuestieLoader:ImportModule("QuestieDB"):GetQuest(4962).nextQuestInChain

/dump C_QuestLog.IsQuestFlaggedCompleted(4962)
/dump C_QuestLog.IsQuestFlaggedCompleted(4963)
/dump C_QuestLog.IsQuestFlaggedCompleted(1799)

Also as sanity check: You're using v8.2.1 and still play wotlk, right?