On Sun, 5 Feb 2017 11:58:11 -0800 (PST)
home owner wrote:

In 2005, I bought a Panasonic DECT 6.0-Series Cordless Phone System
with Answering System (KX-TG1033S) which includes 3 handsets, 1 base,
and 2 chargers. In September 2015, I installed Panasonic HHR-75 (700
mAh) AAA Ni-MH Rechargeable Batteries in each handset.

When an incoming call goes to the answering system, a buzzing sound
occurs. The buzzing sound is also heard when I listen to recorded
messages.

What is causing the buzzing sound?
How can I resolve it?
Or would it be best to buy a new phone/answering system?

That is the sound of the NSA making a copy.