How to remove a stripped screw from an iPhone 4?

Question

Since APPLE is so kind as to tell me "You broke your iPhone's home button, you can replace the phone for $200 I decided I'll just open it up and replace it myself!" I just recently went to replace my iPhone 4 screen/home button and find a stripped screw that's connected the battery to the phone. How would I remove such a small stripped screw?
I heard using a Screw Extractor, but what size would I need to do this?

Answer 1

Thank you, that's very helpful.
I was able to get this to work for deleting single song, but it simply ignored me when I tried to delete whole albums or artists. As there are many thousands of Christmas tracks, deleting one by one was not an option.
When I first started to research this I was not able to find any posts on the subject (because I did not know about the left swipe to delete gesture and so did not search for it). Now that I know I found this post which gives a number of different ways to do this:
http://forums.macrumors.com/archive/index.php/t-1276850.html
At first I tried this option:
If you are trying to batchdelete all music on an iOS device, it can be done.
1) Settings > General > Usage
2) Let the Storage settings load.
3) Click on Music...on next screen, swipe anddelete.
That does zap everything, but it suited my purposes. At first I though this was working, lots of tracks started to go back into the cloud (although this does not happen allat once, it seems to do it in the background over a period of time). The usage screen said I had free space on the iPad, but when I plugged it into iTunes the iPad showed as full and the tracks were all still listed under music.
So I tried this:
You can turn off iTunesmatch and then sync a very small number of tracks via iTunes, which shouldreplace the downloaded tracks with the synced tracks. Then turn Match back on.It's a pain but that is the only way I have found to mass delete.
Which did the trick, but is something of a nuclear option.
Looks like Apple have some work to do here. Deleting a track at a time or everything in one go is too clumsy. You need to be able to delete Albums, Artists or Genres in the sameway you can delete songs. I wish there was a way of reporting bugs like this to Apple, but short of signing up to be a developer, there does not seem to be away. If anyone reading this is a developer, perhaps you can get a paste the text into a bug report.