Hello to you too, and welcome to Toyota Nation! I don't have an answer myself to your reverse noise, and if your search didn't turn up any relevant threads I'd say go ahead and post up a new one to the Corolla forum and see if the other owners have experienced that or have an answer. I had a TR7 once that did something similar--I had to engage the clutch and wait about 5 seconds before putting it into reverse, or else have the gears grind

--and I attributed it to a flywheel problem. I ended up living with that 5 second irritation instead of trying to fix it, especially since it was a Triumph.