If the client is indeed connecting to Exchange via EWS, there is a way to discover the UserAgent being used for this client. As long as it is identifiable (not a thing in a hosted service, btw.) you can block it via Set-OrganizationConfig
.
Use a log parser to look at IIS logs on exchange server to discover an app's User Agent string. Armed with this info, you may use the following on Exchange 2010 and above:
Set-OrganizationConfig -EwsApplicationAccessPolicy EnforceBlockList -EwsBlockList @{Add="UserAgent/*"}
Wildcards can be your friend in the User Agent block list, this really depends on what you find in your IIS logs.
You could also block this per-user by using Set-CasMailbox
instead of the org-wide 'Set-OrganizationConfig`
Reference: https://blogs.technet.microsoft.com/matabra/2012/08/23/block-mobile-apps-that-use-exchange-web-services/
I also wrote about blocking a specific app here: http://blaughwtech.blogspot.com/2015/07/block-microsoft-send-app-in-ews-policy.html