Pruning instructions in my book are "prune lightly in late winter to remove any dead or damaged wood, and to reshape". If you want to take the dead flowers off, just clip beneath them, where they join the stem.

I remove the dead flowers off our carpentaria and tidy it up too. They can get a big leggy and straggly if not kept under control. I get a lot of brown marks on the mature leaves some years, and it seems to respond to epsom salts watered in.