The 53112-20260 Grille will work just fine on the 2000, 2001, 2002 Celica front bumpers.
And although there is no need to remove the entire bumper assembly to install the grill, it sure makes it easier to do. I've installed quite a few of these grills, and never had to remove the bumper.
The front bumper already has all the hardware and attachment points to make adding this grill as easy as:
From under your celica:
a) unscrew a few locations from the front of your Celica's under plastics. do not remove the plastics, just fold them back.
b) insert the new grill in to place (snapping the plastic hooks over your bumper's edges)
c) re-attach the under plastic nuts, threading through the holes in the grill and plastics.
Basically, the grill install is much easier than doing an oil change
Edit: 10mm socket