My boyfriend extracted the stripped screw that held the battery in place by using a pair of nail clippers as pliers. He gripped the edges of the screw with the head of the clippers (I can't remember if he used a concave or convex one but either should work) and twisted until it came loose, then replaced the battery as shown in this video
The 4s battery swelled a year and a half after getting his phone, but when he took it to the Apple store the sales rep claimed they couldn't replace it due to a potential explosion and his only option was to buy a replacement phone (of course) for $150.
He ordered an iPhone battery replacement kit from Amazon (http://www.amazon.com/gp/product/B009SJG...) and tried the screwdrivers that came in various repair kits but they were all too big, and also attempted the superglue method but couldn't get the screw to stick. Thankfully he was able to replace the battery after discovering the nail clippers could work as pliers, and nothing exploded (in yo face, Apple store!)
Hopefully you'll be able to replace the battery yourself instead of paying the Apple store any more $. Good luck