I suspect that your 'seed pods' are flower buds. You wouldn't have seeds unless you had already had flowers and anyway, chives don't produce pods, more of a dehydrated- looking version of their flowers. Cut them off or leave them as you wish. The plant will be a bit more vigorous if you remove them. You can eat the flowers.

Check the link and see if this is what you have.

Here is a link that might be useful:

Sure, first comes the flower then the seeds develop. You have to let them mature to be viable.
But if you wait too long, they will fall off.
Viable seeds will be hard and black color. You can save and plant them in the fall or spring.

Let the flower heads dry and get papery before collecting the mature seeds.

The flowers are pretty and one of the early bloomers in my gardens.

FataMorgana