CPC and HT-286

[voxabox]

I happened to be home yesterday when someone called.
I let the answering machine handle it. The caller hung up; however,
I ended up with an annoying "off hook/reoder" pulsing Klaxon tone recorded on my machine

updated:
I thought the annoying "off hook/reoder" tone was recorded only when the callers hung up without leaving a message. It got recorded when the callers left a message as well - at the end of the recorded message

It seemed that the HT-286 was "too slow" in detecting that the calling party has disconnected.

I experienced the same issue while I was with another VOIP provider. Fortunately, I was able to fixed it by tweaking the "CPC delay" and the "CPC duration" on the linksys/sipura ATA.

Looking through the HT-286 documentation, I did not see any provision for CPC.
The "Onhook Threshold" seems to be the closest thing.

updated:
further reading tells me that I was wrong about "Onhook Threshold":
The "Onhook Threshold" is for the hook flash/call waiting purposes!

Assuming that the HT-286 does not allow any CPC tweaking, is there anything can be done with the SIP server?

Yeah, I know, I'm olde schooled, but I still like to use the answering machine
(so that I can screen calls)