You'd be very lucky if you could get the original shape back on this case back. I'm talking the diameter and flatness.

That being said, I would attempt to flatten the rim out by using something hard such as wood or aluminum with a hole the size of the underside of the top lip, just clearing the lip that snaps into the case. I would use a flat piece of wood to tap (not tap WITH the wood, use a small hammer to tap ON the wood) on the top of the case back to nudge the lip back into flatness. This may not bring the diameter into round though, which is just as important to keep the back pressed into place on the case. I would use the I.D. jaws of a caliper to check the inside diameter of the back to see if it is still warped.

The other thing that can be done, if you want to save the watch, is find a used watch of the same model and steel the case back.

 

The caseback will have to be trued up, as Mr Dennis points out. This is not a beginning task, but you might get lucky. You will have to determine where the back is out of true and work to move the metal back where it belongs. A truing block, wood, hammer, and maybe a dapping block will help.
You might be able to source a replacement from a parts watch (use complete reference number to search). Otherwise, this will cost more with a jeweler or watchmaker than the watch is likely worth.
Patience is a key attribute in watchmaking. Adrenaline is an enemy.
Regards, BG

 

erudite...Hello.

This is what I'll call 'fussy' work...you will need to deal with several surfaces to get everything to where the back will actually snap on, and stay there. It looks like there's not all that much damage / distortion, and what there is, should be removable...with some Luck and Patience. A flat block of steel / a brass-faced hammer / a small, stout pair of pliers / a fine file or two / some metal polish...and, you'll probably get to where you want to go.

Michael.