The seed pods are often called scapes. Typically, it is recommended that you cut the scape off where it meets the bulk of the plant so that the plant's growing energies can be focused on the bulb. Scapes, incidentally, are often used as an early-season substitute for garlic in the form of greens. You can also use the small bulbs inside the flower as garlic.
Garlic is typically ready to harvest when most of the plant has turned brown. It sounds like yours is close to being ready to pick if not ready to pick. You don't want to leave it in the ground too long. One way to judge is simply pull one out and look a the bulbs. If they look mature and are papered over well, you can probably go ahead and pick the rest, dry them in a warm, dry place (keep them out of rain) and then eat or store. I"ve cut and pasted information from UK Extension's vegetable gardening in Kentucky guide, which is very good. Here's a link to the entire publication: http://www2.ca.uky.edu/agc/pubs/id/id128/id128.pdf I hope this helps. Good luck and happy cooking.
There is only one species of true garlic.
Allium sativum, an herbaceous biennial
which belongs to the lily family. It is usu‑
ally divided into two subspecies ophioscordon (hardneck or top set garlic) and sativum (softneck garlic). Hardneck garlic pro‑
duces flower stalks called scapes and bul‑
bils at the top of the stalk. Soft‑neck garlic
usually does not produce bulbils but pro‑
duces larger bulbs with more cloves per
bulb. The cloves which make up the ma‑
ture garlic bulb are used for propagation.
Propagation from bulbils is more difficult
and requires two years to produce mature
bulbs. Hardneck garlic cultivars usually do
better in colder climates and produce larg‑
er cloves that are easier to peel.
Planting and culture of garlic differ little
from onions, but many gardeners believe
garlic is more exacting in its requirements.
No one cultivar or cultural practice is best
suited for every situation. An open, sun‑
ny location, with a fertile well drained soil
that is high in organic matter is desirable.
Fertilizer is usual applied beginning in the
spring as side‑dressings every two weeks
until bulbs begin to form. Garlic is day
length sensitive and begins to bulb around
the summer solstice. In Kentucky, it is best
to plant garlic in October and early No‑
vember. Plant individual cloves root end
down and cover with two to three inches
of well‑drained soil. Allow six inches be‑
tween sets. Mulch helps provide winter
protection and conserves moisture during
the summer. On hardneck garlic remove
any flowering stalk that forms to increase
bulb size. During the growing season gar‑
lic needs 1 in. of water/week. Stop water‑
ing about 2 weeks before harvest.
Many gardeners enjoy eating the green
shoots and leaves of garlic plants. Howev‑
er, cutting them continuously inhibits bulb
formation. By early June, flower stalks may
appear and should be cut back and discard‑
ed so the plant’s energies can be direct‑
ed toward root and bulb formation. Some
people eat the flower stalk. Bulbs begin to
mature or ripen in mid‑July and early Au‑
gust, and the leaves become yellow and the
leaf tips turn brown. When the leaves have
yellowed, lift the plants and dry the bulbs
in a partly shaded storage area for about
2 weeks. After drying the tops may be re‑
moved, braided or tied and then hung in
a cool, well‑ventilated spot. Dampness in‑