Depends?
It depends on what type Challenger you have.  You list that you have the Challenger 2000.  Is that the year model?  
If you have the Challenger 1800, then your running the M-2 engine, the grate is suppose to be fixed.  
If your running the standard Challenger, then yes, the grate is suppose to move up and down.  It's a feature they added called the "weedless" system.  There should be a handle under your dash somewhere, that you pull on.  This allows the grate to drop for cleaning out the weeds or trash. 
If your having a problem keeping yours up, then the cable may be broken.:cheers: