So, I'll admit that I just learned this. You can right click on the duplicate object/process reference and click 'Remove From Group'. If there is already a reference to the object/process in another folder, it will simply remove the reference that you just clicked on. If there is no other reference to it (that is, there is no duplicate), it will place an object/process reference in the Default folder.
Kudos to my co-worker for noticing this option. I've spent an obscene number of hours working and playing in Blue Prism and never noticed this before. I also assumed it would require an operation on the database tables. That does work too of course. You can delete the duplicate entry in the table called something like BPAGroupProcess.
Dave Morris, 3Ci at Southern Company