Online conference participants hear echo when cinema display is connected via mini-displayport, even though I am using headphones with mic.

When I use Google Hangout or GoToMeeting, other participants in the meeting hear an echo of their sound -- loud and obtrusive. When I mute, it goes away.

• This only happens when I am using my Apple Cinema Display 27" (recent vintage) connected via the mini-displayport (natively, not an adapter).
• On my end, i don't hear their echo, but I do hear waves of squelching -- basically it sounds like their end is trying to adjust their input down to account for what it thinks I saying, even though I'm not talking, it's just the echo making that happen.
• Sometimes this doesn't occur -- it seems to crop up intermittently, but happens around 75% of the time at some point in a conversation.
• I am using iPhone-compatible in-ear earphones with built-in mic; the earphones are the rubber seal type, so there's no sound escaping them that the system should even be able to hear.
• I have my audio set up for "Headphones" as output device.
• Input device is set up as "External Microphone" -- this part confuses me because even though I know my Cinema Display has a microphone, the OS seems not to list it as a separate input device. So I wonder if it's getting confused trying to use both the cinema display's mic *and* the earphone mic? (see dropdown image)
• OS version 10.20.2; Macbook Air 13 inch, "early 2014" and Apple LED Cinema Display 27inch
• Earphones are skull-candy brand iPhone compatible (with built-in mic), plugged into the macbook air's earphone jack. (without the display connected, this has always worked fine -- and with a prior non-apple display that had no mic/camera this was not a problem)

This is an ongoing issue in our office, in fact ... especially troublesome in client meetings.

I haven't tried other configurations, other than when using the Cinema Display's USB connector, the same thing happens.

It also happens even when I'm not using the "USB PnP Sound Device" you see listed in the dropdown here -- that's something I use for controlling music output to my desk speakers.

A general question: is there no way to control the cinema display's mic and/or camera more directly?

(EDITED TO ADD: Ok I see in the Cinema Display manual, there should be a listing for "Display Audio" in the input list, but my SysPref panel has none listed. See other screenshot. I wonder if this is the problem??)