For white glues, you soak the entire system in a shallow bowl of Autoglym Intensive Tar Remover for 20-30 minutes and the glue lifts out & turns to jelly and you then wash & rinse the system as per normal.

But Ultra Hold is a different type of glue and it breaks down with acetone, so you soak it in a nail varnish remover.
Surprisingly this won't harm the system.