Agree with others - spooger will almost certainly break if you try to pry it out using just that and you can't pull hard enough on the plastic tab. Even on my 2 year old phone, the glue was still *quite* good at holding the battery in.
I used an equally small flat-blade screwdriver and gently walked around the battery lifting against the bottom plastic and the edge of the phone being careful NEVER to touch any of the flat-cable wires. While you can pry against the bottom since there is nothing under it (just double-check since there are some wires running along the side of the phone and the pressure you need to remove the battery would damage the wires if you pryed on them), you need to be careful against the edge of the phone. It's cheap plastic. You can pry against it, but I dared not use more force than enough to start hearing the adhesive start to rip/creak loose. SLOWLY walking around the battery at safe pry points several times finally loosened it enough that I could pull it out. GO SLOW.
As a help to doing this step, put your thumb/fingers around the phone around the middle so it's cradled in your hand. Keep your fingers wrapped around and resting gently on the top of the screen with your thumb and the first few fingers. See how his thumb is sitting on the edge like that, but ready to 'catch' the screen when it comes up? Do that with your thumb and the tips of your fingers on the other side.
Now carefully use the suction cup to 'walk/rock' the screen out with a left-to-right while pulling up motions. With your fingers gently clamped around the phone and providing a little pressure on the edges overlapping the screen when the screen comes out, they'll catch the screen before you pull it up too far and yank the cables out.
Shesh - why doesn't the first line of step #1 say "Turn off your phone" by holding the power button down and shutting it down. I know you don't HAVE to do this, but it certain didn't feel right opening a device while the screen was humming along looking at me.
GREAT tip about the flat fridge magnet to lay out and hold the screws as you take them out. I would have certainly dropped a screw or mixed them up if I'd not used this tip.
I just performed a battery replacement on my 3GS last night. I got everything plugged back in and it went smoothly - but when I turned it on - the screen would backlight, but no icons/images. Plugged into a computer I could see all my music/etc - so I knew I didn't brick the phone; but no images after opening and re-seating everything 3 times.
Saw someone else had trouble with charging until he restored factory defaults so I figured I'd try that. I told iTunes to restore factory defaults, and right after the update - screen appears. Why a software reset would bring a screen back from a battery change makes NO sense to me - but that did it.