The cURL command, as you know, performs the client side of an HTTPS SSL handshake as appropriate. In any SSL handshake, the server sends its certificate to the client and the client must then "accept" that certificate as valid and trusted. The -k option simply tells cURL to ignore validity and trust checks. In lieu of that you'd need to provide a way for cURL to validate (and trust) the server's certificate, usually by way of a CA certificate or certificate bundle using the -cacert option.
As the HTTPS monitor doesn't have an option to specify a CA certificate (or bundle), depending on version I believe, it should imply the same -k option and ignore server certificate validity checks.
Are you not seeing this behavior?