I don’t know if there is a good way to do this.
I suppose you could remove the Thing in PaperUI and it should go back to the Inbox. I’ve not tested this so cannot guarantee that it will go back to the Inbox though.
If you remove the links to the Items the bindings should be less concerned about trying to talk to those things since there is nothing in OH that cares about them, perhaps that will reduce the logs.
Beyond these two ideas, I know of nothing that would let you do this.
Ultimately, if it is primarily the logs that you are concerned about, you can push that binding’s logs to some other file and/or use filtering as you look through or watch the logs.