I have lower level alts with myriad level 615 items retrieved from Follower missions through the garrisons which are unusable until level 100.

The button cheerily taunts me with the items which I cannot open, causing me to cry.

Please do not let the addon make me cry.

Which items specifically?

iLvl 615 Munficient items.
114109
114068
114063
114058
114066
114059
114057
114060

ExtraQuestButton does not do anything with items that would not normally appear in the objective tracker.
If you are unsure about which mod is doing that to you, use /fstack to find out.

Sounds like Openables or some other addon that gives you a "click to open the clam/box/other thing" button.