You’ll want to harvest the garlic scape once it’s grown above the rest of the plant and just before, or just after, the top of the stem forms it first loop.
If you let it continue coiling around, the scape will toughen up (making it not nearly as palatable) and reduce the final yield of the garlic bulb.
It’s best to harvest scapes in late morning to afternoon when it’s dry, that way the cut has time to heal and is less susceptible to disease. Use pruning shears or snips for a clean cut, and cut the stem at the point where it meets the topmost leaf of the plant.
If you want to maximize your garlic scape harvest, you can pull it out with your hand. Grasp the stem below the seed pod (which looks like a long pointed cap) and pull slowly and firmly upward.
The scape will release with a pop, and you’ll end up with the full length of the stem, including the tender lower portion that you otherwise wouldn’t get if you simply cut it off. If the scape snaps off before it pulls out, just wait until next time and pull the remaining stem when it’s grown taller.