Answer: If you have annual poppies and you want them to reseed themselves, leave the pods on the plants until the seeds are ripe and the pods burst open. If you do not want them seeding about, remove the pods.
If you have perennial poppy plants, you may want to leave the pods on as an ornamental feature, or you can trim them off now. Eventually the plants will die back and go dormant for the summer, at that point you can trim away all of the dried foliage as well.
I hope this helps.
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