That sounds like the dealer trying to upsell you a new plug that you don't need. You can replace just the plug instead of the whole unit, or maybe just get an adapter. A friend of mine had a similar issue with their EVSE, and they found a compatible thermistor-equipped replacement plug online. Just make sure you get one rated for the same amperage as your busted one.
You’ll probably need a screwdriver, wire strippers, and a little patience to swap it out, but it’s worth it for the savings. Or, if you’d rather not risk it, an electrician could fix it for way less than replacing the entire charger.