A 'tidy' gardener would often cut off the old stem. On the other hand the brown stem and seed pod can look quite attractive through the winter, especially for the taller Siberian irises.

I agree with Bulb. However, if you have 'rebloomers' I would clean them up for the second flush of blooms.

some iris are grown for their seed heads/pods eg I.foetidissima

I often leave them to gather frost too Bulba.

Even if it isn't a rebloomer, next year's crop of flowers will be heavier if seeds aren't allowed to form.