Ouch. If he did a good job gluing, then the best idea I can come up with would be to drill holes.
On the inside of the drawer, try your best to line up with the where the screws should be holding the handles on. I'd take a 1/2" drill bit and drill down through 'most' of the inside board, I would guess the board is either a 1/2" or 3/4" board. so drill to just short of the depth, or just to it (stop if you hear metal on metal!). An easy way to do that is to measure the distance on the drill bit and put a piece of masking tape so when the tape reaches the wood stop.
If you measured right, the screw head should be there and you might need a little knife to clean up the hole. With any luck there won't be glue in the screw heads otherwise you might need a small sharp tool to clean them out as well.
After that you should be good to go.