It didn't leave the quest section tab and the mod to let me drop quest items isn't working. It looks like it was dropped but nothing appears on the ground and it's back in the inventory afterwards.

The trophy and other quest items I could find use mh701 so I was thinking it would be mh701_sharley_lure but I can't figure out what it actually is.

The trophy is q603_sharley_trophy, so try q603.

That one is the conserved trophy for Avid Collector.

Apparently the bait is automatically added to your inventory once you acquire the formula during the quest. So even if you remove it, it will reappear.

I haven't redone the quest to unlock the special mutation abilities on NG+ so maybe using cleardevelop and beating the quest will unlock them properly again, so I can just use the console commands to level back up and clear out the quest items to delete it. I was planning on that as a last resort but if no one else knows of a way to get rid of it, that seems like the only option left.