I have a CTI Route-Point which has 8888 as extension. The route-point is pointed to a route-list and then to a route-group which has 5 members. The members of the hunt-group are not able to see the Caller ID/Name for the incoming calls (PSTN). All they see in the phone screen is the message "forwared to 8888". This is not what we want, we need to see the Caller ID/Name. Please note that this issue is only for the calls distined for 8888. I am using the Time Period Routing.
Normally, you would only "front end" the Hunt Pilot with a CTI-RP if you want to show the Forwarded CLID (the actual CLID should show once the call has been answered). To receive the direct CLID you would just make 8888 the actual Hunt Pilot DN. I just tested this out in the lab :)
Hope this helps!