Delete references from online search without losing them locally?

I can’t figure out how to completely “trash” (including empty) the results from an online search without losing them locally. If, for example, I search for “Cat in the Hat” at the LoC and move one result to a group, how do I completely clear that search and still retain the result I put in a group? Each time I trash all the references, the group reference is trashed as well. This is *supremely* frustrating, since I’d like to just find the reference I want, save it locally, and then clear *every* results from the LoC search. So far, I can’t figure this out, and I’m about to recommend another piece of software to everyone I know rather than keep dealing with this, lol.