Check out this article http://www.premierguitar.com/articles/5_Essential_Jazzmaster_Maintenance_Tips
specifically this part , you might be able to screw it to a board and let it sit for a while or you might just need a new pickguard.
5. Replace your pickguard.
If you've got a vintage Jazzmaster with the old-school celluloid pickguard, these things tend to shrink over time and you might find it impossible to adjust pickup height as the covers are being squeezed by the pickguard. There are only a few solutions to this. On Thurston Moore's guitars I've dremeled out the pickup holes a bit to make them fit, but ideally you can swap out the guard with a new one.
Important: if you remove a vintage celluloid pickguard, mount it (with the original screws if possible) to a piece of wood so it doesn't shrivel up too much, in case you ever decide to put it back on your Jazzmaster.
As far as new pickguards go, the real Fender tortoiseshell-style is pretty passable, or another cool solution is an anodized aluminum pickguard from tone-guard.com. Sure, you don't want to lose any of your axe's mojo by changing the guard, but the whole point is functionality, and you've got the old one properly preserved in case you ever want to go back.
