Be calm, and search for other similar questions. It happens more than you think. I too passed under that crucible.
I can see the screws are cramped. Hopefully, it seems you can get a slight grip on the screwhead. So, even if you end up scratching around the screws, that would be no big deal. But we'll try to avoid doing that too.
Torx screws and Pentalobes are the easiest to strip, but Philips 00, on a Macboook (Pro), seems made out of butter and cocoa so prevention is in order: your screwdriver is obviously worn out. I stripped badly a Philips 00 with an old jewelry screwdriver, so I bought a new one from a reputable source. If you're not constrained by mailing fees, iFixit has good ones.
Granted you're sure to avoid spills on sensitive parts of your Macbook, there are lubricants that loosen screw enough to help in the operations. Otherwise, it's better act without.
But return to the issue you've got at hand. In order of destructivity to the screw and item you'd need to achieve that (I'll give you later the most effective) you may:
- If there's still at least a couple of recognizable grooves on the head, poke and pry them with a flat screwdriver, angling it and trying to twist the screw out.
- You can also try using a slightly bigger Screwdriver, with a bigger handle and a longer shaft, for more torque
- If you've got something to increase the grip, and the screwhead is at least half recognizable, use it. The skin of an old baloon, or some special concoctions you can find on Amazon, acting as a temporary glue. The screwdriver will be able to grip enough to let you loosen the screw, and then you may finish the job with tweezers, pliers or fingers.
- Failing all of that, you're entering in the "danger zone", that is, the point where the screw has to be physically damaged and/or you're going to face expenses to let the little bastard go out. First of the danger zone is the '''acquisition of screw extractors'''. They've special heads that burrow in the half-grooves you've left, allowing you to twist them out
- Failing that, but only if you managed to dislodge at least partly the screws (even if, cramped as it is, it'll need a really strong and firm hand), you could grip them with the ESD Screw Extracting Pliers, the smallest measure. If you've not got handy, you could use a very small wire cutter, but be forewarned that the job will end more messy: while in both cases the screw will end with a dent, bent and squeezed head, the SEP allow for a better grip and torque, the wire cutters, made for a different task, won't, and you'd have to squeeze until they cut a "groove" at the sides of the screw. At that point, you'd likely scratch around the hole (no big deal) and nick the cutters itself, granted the "half-dome" head doesn't make things even harder. The SEP remove that risk.
- Failing that, or if you're unwilling to get those items, you could use a Dremel with the smallest rotary cutting head you've got, and cut a slot in the screw. Then you may be able to use a flat screwdriver
- Failing that, you could coat an old screwdriver with a tiny amount of Gorilla Grue or strong glue (avoid spilling!!) and let it cure on the screw. Then remove it.
- Failing all of the above, but only failing all of the above, use a drill of roughly the same diameter of the screw shaft, and drill the head out, removing the shaft later with pliers.
The safest course of actions passes through the use of the Screw Extractors and the SEP, after evaluating that the screw is unable to be removed with other screwdrivers.
The drill is the last resort, use it only after everything else fails. The glue method and the dremel one seems commonplace, but the Extractors can always be kept for later occurrencies.
Also, remember that you're going to need a couple of new screws. So, a visit to the Apple Store is a nice try.
So it would be nice to pay them a visit: Apple sells screws in sets and kits, so Apple Technicians have lots of spares to share for a nominal fee. Also, they could feel helpful and help with the removal, by the means of an out-of-warranty repair or some additional hints.