Hi Paun,
Sorry about the delayed response on this.
I've never seen this issue in relation to the Integration Fields write API.
I talked with the team and this is related to the fact that you're trying to send information through a react app in the browser. This isn't the intended use of this API, it's meant to be sent from a server or using a CURL request. It's the expected behaviour that chrome or whatever blocks it with the CORS error.
We could discuss further with the team to allow requests coming from the browser. I'm not sure it's something that the team would want to do, but it would be really useful to understand your use case here so that I can communicate it with the team.
Thanks.