I took “Romlyn Dreth's Silver Emerald Necklace” off a dead thief after the Riften Guards killed him. The game will not let me get rid of it, because it is a quest item. However, I can't get him to take it back. Would somebody please tell me what quest this necklace is involved in?
Your item is probably a radiant item.
For many repeatable quests, Skyrim auto-generates variables, like items and locations, to keep it interesting. Examples of these radiant quests are the jobs the Thieves Guild has for the player.
It could very well be that your item comes from one of Vex's Burglary Jobs or Heist Jobs, or one of Delvin's Fishing Jobs, that was auto-assigned to belong to Romlyn Dreth.
Returning to the Ragged Flagon and speaking with either Vex or Delvin might solve the matter.
This reddit thread deals with a similar issue.
Someone with a name remarkably similar to yours seems to have the exact same problem here. The proposed solutions are quite similar, but a noteworthy additional suggestion is using the console command
player.removeitem "item ID" "amount" to get rid of the item.
To find the item's ID - and this I found here - you can use the command
help "item" 0, and replace "item" with a keyword, so in your case Romlyn or Emerald might do the trick.