I'd like to finally know what is going on with Special Arena quests

[Complex]

So! Special Arena quests are annoying, I knew this from the base game where after a while it became very difficult to know for sure what I needed to do to finish all the optional quests, etc. So going into Iceborne I made sure to not complete any Special Arena quests until I had all of them in the optional quests list. I've played the game on and off for a while, have eventually decided to start finishing the optional quests, check the list of special arena for 3 star and I am missing the glavenus one.

No big deal, I'll just capture one! Capture it, no special arena quest. Oh whoops I guess an expedition doesn't work for that, so I capture it again in an optional quest now. Still no dice. Do an investigation specifically for capturing it, still nothing. Search around and people are talking about checking the field guide to make sure you've captured it, out of curiosity I check, I have captured it 8 times! 8!

Clearly I have been coming back to the game over and over and repeating this same thing after just forgetting about it and working on something else. So. What is the deal! What am I missing here? What can I even do?

[AurumHawke]

Glavenus is MR-only so any captures you have can only have been MR Glavenus and its Special Arena quest is indeed MR 3-Star.
Whether you captured it in expedition or quest should be irrelevant (and is here, for this question, since you did both).
Capturing it again didn't unlock it so it's most likely you already completed the quest.

Do you play multiplayer and may have finished the quest someone else posted?
Any other reason you may have already completed it?
Any mods?... They shouldn't mess with it, but could.

Make sure all lower tiers are completed so any quest chains are at or past MR 3-Star. Confirm you have the other MR 3-Star Special Arena quests (which you did) and complete the tier for the completion mark. Check the MR-3 completed section for Glavenus between quests.

Special Arena quests are always available before they've been completed the first time.
Capturing a higher-rank monster unlocks the quest for that rank and all lower ranks - an HR Tobi unlocks HR and LR, an MR Tobi unlocks MR, HR, and LR.