Certainly need to remove the old flowering stems or you will have baby ones popping up all over the place.

Sisryrinchium is very tolerant of almost anything you could do to it. Leave it, apart from dead heading and a feed, for now and you might get some more flower. If the clump gets too big at the end of the season, and lots of black leaves. Take it out (not deep rooted) and sort out what you want to be in a given place. Easy to split and start it off in a new place too. You can pop some in an odd corner till you decide to bin or use. Sorry OB you posted while i was typing.