You will need to replace this part.
Here is the guide to follow.
The mute switch is connected to the headphone jack, so unfortunately you will need to replace the whole thing. I recommend you buy the part from eBay to save money. This part can be quite fiddly to change, so you may want to consider buying a complete rear housing. However, the complete housings are not OEM, so can cause some problems in the future (although I've used them and they have all worked fine).
If you live in the UK I will change the part for you. I will replace the actual part, not use a 3rd party back ^_^
Hope this helps anyway,