I do not think that TSB applies to 05 corollas.My '05 Corolla started making a growling noise when first started and put in reverse(A/T) at around 33k miles. The sound is like the coolant resevoir or washer fluid resevoir is rattling against the frame or something. I took it to the dealer and he told me that it was the Belt Tensioner, and since I was past the 36 month mark it would be $370 to put a new one on. I told him I would live with it, and he told me that when the belt started squealing it would need attention. Low and behold - I now have 41K miles and it really rattles and the belt squeals! This was a gradual process that originally only happened for a few seconds when cold and would go away. Now the growl or rattle continues for 20-30 seconds and the belt squeal is non stop. I have owned Toyota's for 20+ years, and to me this is an embarrassment to them. I also believe it to be a "Drivetrain" issue because it obviously won't run long without the tensioner.
I called the 800 number and they wanted to know what I thought was an acceptable solution, so I explained why I thought it was a warranty item. So far I have no resolution at all. I did see a note about a TSB, and another guy got his tensioner replaced on his 03 well after the warranty, so I am going to follow up. It sounds like these tensioners have been a problem for quite a while, hard to believe they haven't addressed them.