Hi Andy,
I echo most of what has been said above. Your initial screenshot indicates the reception of a Mode-C response from a transponder. This could be from another aircraft fitted with an actual Mode-C transponder, or a Mode-C (altitude) response from any nearby Mode-S transponder. If you are running a transponder of any sort in your aircraft, your ‘Bearingless Contact Setting’ for Mode-C/S MUST be set to ‘Mode-CS + Filter’. If - as in your case - the filter is not set there is a high probability that the ‘Random’ Mode C responses are from your own transponder.
If you wan’t to reduce Bearingless Alerts from Mode C/S aircraft generally, you could try reducing the Mode-C/S Horizontal Sensitivity to ‘Short Range’ and or the Mode-C/S Vertical Display Range to +/- 1000ft - if you are happy to accept the increased level of risk as these aircraft will be considerably closer by the time you get warnings. (In reality, it is perfectly acceptable to fly on the Short Range and +/- 1000ft settings, but DO NOT risk using the Ultra Short Range Setting unless you are fully aware of the potential effect on warnings.)
My second comment (sorry Ian) is that the Positional Contacts Settings Horizontal and Vertical Display options should ONLY be used if your Electronic Flight Bag (Route and Traffic Display System) doesn’t have it’s own Horizontal and Vertical Display Range Settings (most do - in which case you should leave the PAW ones at ‘Display All’ and set your chosen restricted ranges in your EFB Settings). The ‘Select Audio Warning Zones’ ranges BTW only control transmission of PilotAware Audio Alerts, and will have no effect on audio alerts generated directly by EFB’s such as EasyVFR or SkyDemon.
Hope this helps clarify the situation.
Congratulations on your PilotAware Performance - an excellent example. I take it you have external antennas fitted to your Eurostar. Well done!
Best Regards
Peter