As illustrated in the following image, echo during a Remote LiveShare or Interview session is caused by one (or both) of the devices picking up sound from its own speaker. Most devices and operating systems have built-in echo cancelation to reduce this, but it's not always perfect.
Generally speaking, to minimize - and hopefully eliminate - echo, it's recommend that both the moderator and participant wear headsets with a built-in microphone. Although more rare, echo could still occur even if you are wearing a headset, if the participant and/or the moderator has the volume loud enough for the sound to leak out of the headphones and be picked up by the speakers. In addition, if one or both of the devices being used doesn't have great echo cancelation built-in, you may still get some echo in your session.
If you're both already using headsets and still experiencing echo, we'd recommend you try the following:
Verify that you aren't simultaneously using any other platform/functionality that is also uses audio (e.g. Zoom, FaceTime, etc)
Check your audio settings and try adjusting the volume and sensitivity of your microphone & make sure that the device is configured to us that headset for both input and output
Try using a different headset or even try using no headset at all. While rare, it's possible that some lower quality headsets may actually cause more echo than just using the device's built-in microphone & speakers