Very high volume settings may cause noise from the speakers to be picked up by the microphone. This creates a sound loop that gets louder and louder until you disconnect the headset. As such, you should lower the volume of your headset by pressing the "volume down" button on the adapter.
Another source of the problem may come from someone else in your Xbox Live chat room. that person may be having feedback problems and is transmitting those sounds to all the people in the chat room. You should be able to see which person in the chat is transmitting the feedback; ask that person to lower the volume or unplug his or her microphone.
If you are still not sure what is causing the feedback, check out the [[Xbox One Stereo Headset Troubleshooting|troubleshooting page]].