
You can disable the ability to see recordings in the WebClient via the 3CX Management Console >> Extensions >> Your Extension >> Phone Provisioning >> drop down under Your Phones and select 3CX client >> Scroll down and uncheck Show Call Recordings.If 3CX can not disable the download button in the webclient

No, this is not possible. In 3CX you can either see, hear and download the recordings in the WebClient, or, not see them at all.Sorry, it seems that the requirement cannot be realized, and the requirement is:
The users can hear the recording fies, but they cannot download the recording files. Or if anyone downloads the recording files, they hope to know who download the recording files.
Founded in 2005, when VoIP was an emerging technology, 3CX has gone on to establish itself as a global leader in business communications.