Thank you!
This custom CSS code will resolve it:
[html].proinput form {
border: none !important;
}[/html]
You can apply this code to your theme custom CSS field (if it supports it) or use the custom CSS field on the search plugin back-end. Make sure to clear your site cache (if any) afterwards, and reload the page by hitting CTRL + F5 keys (to clear the browser cache as well).