This may be happening because you have your recording settings set to stereo mix, they may have it aswell, so what you're hearing from them is yourself and them talking, so it will appear echoey.
To change your settings:
Press the little volume icon, go to Options > Properties, press the recording button, and press okay, then check "Microphone", turn the volume up full, then ask the other person to do it.
See if you still receive the echo, if you do, then come back
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