Only if you have the "listen to this device" option ticked on in the microphone settings. If that's not enabled in the OS or any apps you're using should they have their own option for it, something fucky is going on.
Is it a USB headset? If so I'm guessing there's some proprietary software for it with those options
If it's analog (two aux plugs), then you might be getting bleed over....though I think that's less likely since the mic signal hasn't been amplified yet
There're a few things that can cause this. The headphones themselves may have a feature that enables it which you should be able to disable. Otherwise, you may have it configured in your os.
Did you install anything to use them? If so, perhaps the turtle beach software has a setting for this. If not, which OS are you on? Windows 10? 11? Linux?
If you using an audio interface this could be "direct monitoring" which just passes through the microphone audio to the headphones.
Each interface is different but just searching by the interface model should have a general user guide for it.
Otherwise it could be a Windows setting (Assuming your on Windows 10) under the sound control panel which can be accessed by:
Searching for "Sound settings" from the Windows menu,
Sound Control Panel on the right,
Recording tab,
Right click your microphone and choose properties,
Listen tab,
Make sure the "Listen to this device" box is unchecked and apply.