I have the same plants! I cut off all the dead heads, which yes, is a long job. Mine rebloom all summer and even reseed a ton in the areas they are in! I cut off the blooms when the flowers fall out and there are just green little open ended pods on stems. Sometimes I just pull the little pods off with my finger nails.I kept a ton of seeds from mine last year after allowing them to dry out on the plant as well and replanted them around the garden, those also came up! So..yes....even cutting the green pods off will cause them to rebloom next year so I suggest plucking htem and throwing them out if you do not want more of them! Mine started blooming about 2 weeks ago and they will last ALL summer!

Thank you for your help. I'm still a little confused. My stems have both brown pods and green pods on the same stem. The green pods haven't bloomed yet, right? So, I need to pick off all the brown pods in order to keep them blooming. I've never done that before, and they only bloom a short time, but re-seed, and come back like gang busters the next year. So, please let me know if I should only pick off the brown ones, and I'll get started.
Thanks again,
Sally

The spent flower is the brown pods so pick them off. If you want to collect seed, save the little black seed discs inside the brown pods. The green pods are either the new flowers getting ready to bloom, or the end of a blooming flower (easy to tell). If you want to collect seed for re-seeding or trading, save from the brown pods, the seed is ripe in them. Not much to it!