Motorola has a specific tool for removing the heads, but it's just a plastic prying tool. You can do the same thing with a wide blade screwdriver if you are careful. There is the head and there is a plastic mating piece that adapts the head to the radio. Just be careful of the flat ribbon cable that connects the head to the radio. There is some slack, but not a bunch. You can -carefully- unplug the radio end, just make sure you reinstall it the correct way. There is often a black or blue dot on the ribbon cable on one side, and a matching ""0" on the radio body to help with orientation.
Unplugging it from the head side is a bit different. There is a special connector the ribbon cable slides in to. To release it there is a brown side and and a white side on the connector on the head. The brown bit lifts up a little ways and allows the ribbon cable to slide out. When you reinstall it, you insert the cable and push the brown tab back down. The same orientation rules as above apply.
Reassembling is just pushing everything back together. Be careful about not pinching the ribbon cable in the process.
It's actually a pretty easy task to disassemble.
When you get it apart, take a look at the back of the mic connector for a jumper or something like that. Not sure it's the cause of your issue, but it could be.