Paul,
Check the Mailbox or Extension ID of the users and Hunt Group to see if any of them have something other than Unannounced on their Transfer Method. Most likely you will also find that the Allow Transfer Method Programming is set to Yes.
Other than that I am not sure of any other call screening type application that would come over the speaker. My guess is that someone set one of them to Announce-Only unless they have options to send it redirect, answer, or reject the call then it would be Screened.
If I remember the function properly, sorry our customer base does not like this feature, when a call is being transferred from the voice processor it looks at the Mailbox or Extension ID for the transfer method it is suppose to use. If it it set to anything other than Unannounced then it asks the caller to state their name and then announces the name to the user prior to trying the transfer. If a Hunt Group is setup for this then it may send it to whomever is first in the list; not sure.
Well now I have to go play with this feature again to see exactly how it functions to stop my curiosity. My PM is going to hate you now, lol.
Thanks,
TE