How to remove these slot covers?

Lay the computer down on its side, and you should be able to unscrew them from the back of the case - same place as where the top of the card screws in.

Occasionally you'll find a case with an access panel covering the screws, but once you remove that, same thing.

The screws are always in the same place; only thing that tends to be different is whether you access them from the inside of the case with the side cover off, or once in a while from the outside of the case with a separate cover over them.
 
In addition to Capt_Taco, some cases (often the less expensive ones) have the slot covers actually stamped into the sheet-metal. These are designed to that they can be broken off. (Press in from the outside and it would pivot in, then keep moving it back and forth until it snaps off)

Every slot cover can come off of a case.
 
take a phillips screwdriver that matches the + in the cover you want to remove. then just move the screwdriver left and right and they should pop out.


Scratch that...... is there a little door that opens up on the back to slid the top of the card in? I see there are no mounting screws for the card. If thats the case when you pull your card out you should be able to just slide next one out by pulling up on it.
 
ok with the door open see if the cover next to your videocard is loose. if it is the just pull it out. If its not the stick a flat head or philips head in the + on the cover a twist the cover a little it should pop loose and come out then.
 

Okay, I did that, it's sorta bending inwards, but the like holes are messed up. should I continue?