This DIY removes the yellow corner on 2003 Corollas without opening up the headlight
First off to get to the dreaded yellow piece, we'll have to remove the headlight from the car. So lets start by jacking the car up.
Remove the tire
http://i7.photobucket.com/albums/y30...earcorner2.bmp
Next look under the front corner of car just infront of the tire, you should see a bolt and a clip type holder. Remove both of those.
Towards the front or the lip of the car, should be a bolt that holds the front lip. Remove that bolt
Now look in the wheel well, and you should see a number of those clip type holders holding the black cover. You'll need to remove about 3 of those in order to move the flap back.
The picture above shows the location of the bolts that need to be removed. #1, #2, #3, and #7 are the bolts that hold the front bumper. #4, #5, #6 holders the headlight in place. The bumper will have to be lowered slightly in order to get to bolt #6. Start removing bolt #1, #2, #3, #4, #5.

#1 - Move the black flap back.
#2 - You should be able to get to the bolt that holds the bumper
#3 - Lower the bumper enough to allow yourself to get to the hidden last headlight bolt located at #4.