You could try using a bigger screw. If that fails, there is really nothing you can do except get that piece replaced. Are you sure its stripped? Like I said before, you could get a bigger size screw but it might not hold. Your better off trying to order that piece. Is it a bigsby?
Is it the screw that holds it to the body?
If it is a bigsby, what model is it?
http://www.bigsbyguitars.com/intro.html
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This is an easy fix. I'll eat my hat if the screw stripped out before the wood did.
Just take a toothpick, jam it in the hole with some good wood glue like Titebond, trim it flush and put the screw back in. You could go a step further and redrill the hole and fill it with a dowel and then redrill for the screw but the toothpick trick should be more than good enough.