Should I clean old Battery Residue?

Hi Everyone,

I used to sleep with my iPhone 4 in my bottom pillow case. Bad idea- it actually got so hot the battery opened up.

I replaced the battery, and it works, but there is some residue left over from the old battery.

Should I clean this up? Any recommendations on what to use? iFixit recommended windex, but one of my colleagues said that has a chance of harming the device.

Here is a picture of the residue (apologies for the quality- taking this on an iPhone 3G):

http://imageshack.us/photo/my-images/192...

You can see along the left side and you can even see some of the yellow from the battery. Is the left side just adhesive to keep the battery in place? Or is that not normal?

While I'm at it, how should I clean the little contact clip below the battery connector?