Hey @kshibata,
I logged in to your site and I saw you’re using Woo Checkout Editor 2.2.1 and WooCommerce 3.8.1. I suspected that this might be a version compatibility issue but to be sure and save us some back and forth, I tested the setup in my site and I couldn’t replicate the issue you described.
The optional checkout fields were successfully added in the backend/order and the required field didn’t ask for a response when answered correctly.
I now suspect that the issue is likely being coming from one of the third-party plugins in your site. Since it’s a live site, I didn’t test for a plugin conflict because that would interrupt your business operation in your live site.
With that said, I’d recommend you copy your site to a staging server and deactivate all third-party plugins in the staging site and test checking out again. This will quickly tell if one of the third-party plugins is causing the issue.
Thanks.