40D screws stripped

I was attempting to remove the back panel to replace my broken LCD and the two screws next to the viewfinder are now stripped.... I'm at a loss and have no idea where to go from here

I don't think you need to remove anything. Look at the top sticky post, I believe the 40d rear LCD cover is removed by a suction cup

If you're using average or dodgy tools, I'd start by buying some really good quality screwdrivers before going any further - a decent set of phillips head 0, 00 & 000 will get most jobs done here.

If the heads are completely stripped (it happens!) then your only real next move is either grind the heads off or drill them. It depends on what tools you have. In my case it was the heads (both screws) on the IR filter cover that wouldn't budge due to loctite and all I had at the time was small drills. Drill using a 1mm drill until just the head comes off so you can take the back cover off - once the cover is off completely you can go further and drill the remaining screw body out. Use a drill size that will leave the threads intact and then tap the hole to suit the original size if possible. While drilling, get someone to hold a vacuum cleaner close so as much swarf as possible doesn't go into the camera!

10D sensor with stripped IR filter holder screws with heads removed prior to being drilled & tapped: