The quests tied to the icons is actually a questgiver in Dustwallow Marsh
https://classic.wowhead.com/quest=7070/shadowshard-fragments
https://classic.wowhead.com/npc=4967/archmage-tervosh

This is a new bug, just evident today after I updated Questie. Reloads won't affect it. Options in the add-one won't affect it.

I flew out of Ironforge and when I changed zones the icons disappeared

Same problem.
I think it needs hot-fix

Same here.

Integration of the DBM HUD (this shows quests and their objectives directly on screen (requires the DBM addon)) Disable by going into options!

Like Dreijmit said, you can disable it in the settings.

Closed as duplicate of #1296