As before, I've had a big Dropbox clean out, so my old links to the photos posted previously are no longer valid. To get around this being an issue in the future, I've uploaded the photos directly to my iFixit account. Before: After: All Fixed:
You want to remove it using a soldering iron with a small hoof tip, at the lowest temperature your solder can handle. Using leaded solder here will make your job a lot easier. Pop a small amount of flux paste on the existing joints before desoldering, too. I'd recommend against using a heat gun - the kind of heat needed to melt the solder would destroy the plastic flex - or desoldering wick/braid, for a similar reason. It'd be pretty obvious if the new display assembly doesn't already have the sensor, as there will be an exposed copper pad array in that location, ready for a sensor to be soldered onto it. This is what the part looks like:
Yep, the copper is just for additional an ESD ground. There are more than enough solder points on the LCD's back plate that you don't need to worry about additional ground, it's just something added in as a precaution.