What to do with Snowdrops when the pod developes after flowering

Just leave them alone - there's no need to deadhead them. Don't remove the leaves, as they are needed to nourish the bulbs for next year.
If they are in a container, plant them in the garden while they are 'in the green' - that is, while the leaves are still there. It's the best time to plant snowdrops for best results.

The pod contains seeds, if you want more Snowdrops then leave them to ripen (they go black and the seed pod splits open) then scatter them where you want more plants. They take a few years to flower, but worth the wait.