How much does apple charge to replace the back of a 4th generation iPod touch?

Apple does not repair iPods, but will replace the entire iPod for a flat fee; see the Repair Pricing section here:

http://www.apple.com/support/ipod/service/faq/

There are independent iPod repair services that may be able to replace the screen for less. Do a web search for "ipod repair". It is also possible to purchase parts and find instructions on doing a repair yourself, though it's not particularly easy. Note, though, that if you elect to have the iPod serviced by an unauthorized shop or perform a repair yourself, all further support from Apple will be void.

I'd suggest you just get a case or skin to hide the scratches. Either will be much less expensive.

Regards.