Maintaining that status of an item that has been picked up

In this video:

He creates the option to pick up a Lantern and a Teapot. When going back to that same page (where you can pick either of them up), the option to pick up the Lantern or the Teapot is still there, even if you had already picked them up.

Is there a way to remove the option to pick them up again within the same story?

Thank you