Chosen Solution

I was attempting to remove the battery from my iPhone and foolishly did so without properly reading instructions. I did not remove the one screw you are supposed to remove, and as a result I tore the black strip connecting the battery to the connector. Is there any way this can be fixed? Has anybody else ever experienced this problem?

You’re better off picking up a new battery. They aren’t much. Just remove the screw and carefully remove the connector that is still on there. Install in reverse.

As stated by hectordtruong , there is no need to salvage the old battery. You can support iFixIt and buy a new battery from their web store, or pick one up elsewhere for less than $10. Just make sure to remove the screw that keeps the metal plate of the battery in place.