The 3700BQE is a very slightly updated version of the Antec SLK3700AMB so the majority of the features are the same on both cases.
The door on the BQE has 2 plastic latches and 2 thumbscrews that hold it closed. Unscrew the thumbscrews then flip each latch open. You can now open the door and remove it. The right side door has 2 screws only and no latches. To remove it you remove the 2 screws and it hinges open so you can remove it.
There's a picture on
this page that shows the latches on the 3700AMB, the BQE is identical to this.