That does change things a bit, but only marginally so. You obviously aren't going to be able to create a new dovetail joint, unless you have a lot of time and patience and also get a jigsaw. A better route to go would be just buying some wood screws, and drilling pilot holes and running screws through some of the teeth of the back board into the edges of the drawer. Make sure you account for the board sticking out the back instead of being flush with your edge boards in your measurements.

Other thing you could do is just pick up a new board to use as the back instead of one with teeth in it, but the teeth shouldn't give a problem.