GrinMark Synchronizer does not need mailbox passwords of individual users. Instead it uses single Exchange account (called Exchange Service Account) to connect to Exchange via EWS API and impersonate required users. In order to test Exchange connectivity Microsoft developed a handy tool Remote Connectivity Analyzer. It is available online at

https://testconnectivity.microsoft.com/

If you can not connect to Exchange and want to know why - navigate the url, choose Service Account Access option, press Next button, fill-in the form and get the result in XML/HTML format.

Example of test results. Save in XML or HTML format (buttons highlighted).

Beginning of HTML results: