How many miles on it?
I'd be surprised if the rear shoes were worn out, might be just the drum is full of brake dust
pull the rear wheel, look at the brakes
if they aren't worn, blast the drum and shoes with Brake Parts Cleaner (don't shoot it in the bearings)
if they're worn, then you can replace them, but I somehow don't think they will be

Be careful cleaning up. Don't breathe that crap.

When you use the brake,does it tend to lock up and slide the tire?
Unless someone adjusted it wrong or rode around with their foot on the pedal your shoes are nowhere near worn out.
Cleaning up will probably help with the noise for a while.

Modifying the edges has been shown to help.

If it's locking up, say something.

AnalogMan wrote on 06/04/15 at 22:05:27:

page 56 of the owners manual.

2 things cause the brakes to squeal, excessive brake dust is one of them.

Also spend a minutes and get the brake hot to drive off any moisture.

The EBC organic pads and shoes are my choice for new replacements, they are very good.

Most likely your rear shoes are not worn out - the brake just needs to be cleaned up.  One of the things that is really hard on rear brakes is when you wash the bike and then put it away without a ride to get the water out of the brake.....and the water stays in the drum and rusts the steel lining in the aluminum hub.  Then when you next use the brake the rust particles gum up the fiber in the brake shoes.

The mechanic could take the brake drum apart and lightly sand the steel surface in the hub, and the same with the shoes to remove the crap and then clean them with Brake Cleaner.....but at an $ 80 - $ 100 labor rate it might be just as cheap for him to put new shoes in.

Be nice to your new brake shoes....don't put the bike away wet.  Always go for a 10 minute ride after you wash your bike to get the brakes and electrical connectors dried out.

I put new front pads on my bike when I bought it (had an amazing loud squeal).
They started squealing again after a couple thousand miles so I took 'em apart, cleaned 'em up and sanded (emery cloth) the rotor.
The rear brakes started squealing a while back, too.  I put new tires on last weekend and cleaned up all the rear brake bits; it was pretty well covered in brake dust.  I also took emery cloth to the rear drum and shoes while I had everything apart.
Squeal gone from the back now.
Still can't figure out how to keep the pig out of the front brakes.

HovisPresley wrote on 06/05/15 at 07:01:01:

Auto zone sells piddly little packets of 'brake grease'
same stuff (or same effect at least) Customers used to get mad at me for trying to sell it to them, but it's one of the few ('little packets of crap' the company pushes that's actually useful

Weird indeed
My EBCs are probably bedded in by now, no squeel