I only hear the ringing of the TEAM. I have never heard any other ringing (possibly generated by the headset). Only what is sent to the handset is transmitted.
However, you can register 2 devices at the same time. Perhaps check whether there is another device that can also receive TEAMS calls (e.g. PC and mobile phone) and that is also registered on OpenComm. The ringing could be coming from there.

In addition to my question, here is the answer from Shokz:

Thank you for contacting Shokz!

We apologise for the inconvenience this has caused you. The incoming ringtone is the default setting for the headset and cannot be switched off at this time. We are very sorry for this.