It's certainly possible for organizations to set up DNS in such a way that an internal DNS server is only able to resolve internal (non-Internet) addresses.
If internal resources want to reach the Internet in this situation, they are forced to use a proxy to do so.
This is usually for HTTP/HTTPS, and the proxy server generally has access to DNS servers capable of resolving addresses.
It sounds like you have some application that can't use this sort of proxy and has been given direct access to the Internet.
However, you need to know what IP address the connection uses because you do not have access to Internet DNS.
None of the above has anything to do with Check Point, or any specific security gateway vendor for that matter.
It's a function of how the environment is set up.
Once you solve the DNS problem on the client side, there's the matter of allowing access to that IP (whatever it is).
That would be where Check Point is relevant to the discussion.
If the relevant parties want to have a discussion about that portion, they can do so here, through our TAC, Check Point account team, etc.