Items stuck in personal inventory

@Mornimras Thank you for the video, as it was helpful.

• I didn't mean to save them to the gallery... I mean the the library in your game. But yes, if maintaining the relationships is essential you do lose all relationships except the ones in the household you were loaded into the library with, so that's an important factor. 
• If you move the sim out that can delete some things, but this varies.
• Yes, if the item belongs to someone else, or has become 'unowned' it will give you hassles. Maybe you can gift them to an employee... like your maid, gardener, butler, or someone you invite to the lot?
• I did forget to mention that... If you have something spoiled in a stack you have to delete or clean up or whatever option you have for the spoiled items in the stack before deleting the stack. (Such as spoiled eggs, spoiled fish, etc.)

So, by looking at this image I am assuming that you're dealing with personal inventory. Did you try seeing if it would let you include the items if you have muiltselect enabled? 

You could purge this sim's personal inventory via a cheat... First, remove everything from her personal inventory that you want to keep, then:

• Enable Testing Cheats
• Select this sim so she is the active sim.
• Enter the following into the cheat box and press enter:
  inventory.purge

Edit... 
I did an experiment with my sim that may be of use...
I had another sim bring a gemstone to their home and leave it in the home. 

Next, I enabled the sims in the home, and to them, as in your video, it tells in options when clicked on that it does not belong to the sim, though I do see additional options since my sim has experience in archaeology and gemology. However, I was able to go into build mode and use the sledgehammer to delete this gemstone: