You'll need to add manual pressure where the crease is. Pretty sure that part will not pop out.

 

hell with all that get cab corner off rock auto for like 100 and paint it napa can order you paint in a rattle can for like 20 bucks max. then take the insurance check and go from there. as for buying a locker. i have NEVER had my truck be anything but Posi in the rear. its kinda a waste but a bottle of nos and fogger kit might help you lift a little from the whole. just saying

 

^ This guy says exactly what I'd do.
And why would you feel bad not fixing it at a body shop? She backed into your truck, you get a check. Doesn't matter if you fix it or not.
What did you ever end up doing? I have a similar dent in mine.

 

I beat it out with a 2x4. Got it halfway out, not near as bad but could still be beat out more. The way the inner panel is framed kinda limits what you can do.