@Abhay Chandramouli Thank you for reaching out to Microsoft Q&A.
If your Response action includes the following headers, Azure Logic Apps automatically removes these headers from the generated response message without showing any warning or error as documented here.
- Allow
- Content-* headers except for Content-Disposition, Content-Encoding, and Content-Type when you use POST and PUT operations, but are not included for GET operations
- Cookie
- Expires
- Last-Modified
- Set-Cookie
- Transfer-Encoding
Alternatively, you can pull the cookie data using the function in logic app refer to this similar Stack Overflow discussion here.
Feel free to reach back to me if you have any further questions on this.