CDK to add Http headers in the integration request

I have to add a few HTTP headers mapped to the context values that come from the lambda authorizer as shown below

"context": {
    "company_id": "xxxxx-xxx-xxxxxx",
    "Owner":"xxxxx",
  }

and the headers will be sent to the minimal API.

Can anyone help me with the CDK code(.ts) that sends the custom headers to the .net API?