Lay the elevator on a flat surface.

With a heat gun, heat the covering on the side that bows OUT this will initially loosen the covering.

While still very warm, put something very heavy on the elevator to flatten it.

Now repeat on the other side...

Do this a few times hopefully adjusting the covering a bit.

Finally on the side that is bowed out, heat the covering again...

Initially it will loosen but with most normal coverings as you increase the heat, the covering begins to pull tight.

Make sure that the elevator is clamped to a flat surface as you do this final adjustment.

CAREFULLY use heat gun to tighten the covering causing the elevator to hold it's shape.

Remember that you may only be a few degrees away from ruining the covering at this point, so keep the gun in constant motion and moving to encompass as large of an area of the elevator as possible.

Take care NOT to get heat on the edges which will cause the covering to pull away from the underlying wood.

If you have an old crashed plane around, practice on it first... a few practice runs will teach you how to do this.