I presume from what you say, your Corolla is configured with front discs, and rear drums. Maybe it is just what you say, the rear drum is a little rusted. My own Corolla – configured as above – makes a sort of scraping noise from the rear brakes a few days after it has been driven on wet roads, more noticeable if the water is deep enough to splash. And more noticeable if it has sat in the driveway for a few days in between. When the weather dries up and I drive the car regularly, that sound eventually goes away. And doesn’t return unless it rains again.
If you just can’t stand this sound, or are concerned about the condition of the brakes for safety reason, before replacing the drums, ask your shop to measure their dimensions and check for run-out – that’s a measure of how round they are. If those parameters measure ok, new drum are unlikely to help. Instead focus on making sure the rear brake mating surfaces are properly lubed with brake grease, and the brake actuating mechanisms – the master cylinder, wheel cylinders, flexible brake hoses, and parking brake, are all working properly.
One test you could do, while driving at a slow speed in a parking lot, compare the sound when you step on the brake pedal, vs stopping the car with the parking brake. The parking brake on rear drum cars usually only works on the rear brakes.