As anti-static foam isn't reusable, if the laptop has no exposed electrical connections, and the threat you're guarding against is ESD damage to the laptop, and the cost of the foam is small compared to that of the laptop, then use the most conductive foam you can find, namely cushion grade conductive foam.
(I feel faintly embarrassed posting this. You should really get credit for this answer.)
Actually, connecting to the case is probably better unless you also connect the case to earth ground. The easiest way to ground the case is to plug it in, but you don't want to do that until you're ready to power on.
What you're trying to prevent is Electrostatic Discharge (ESD), also known as a static spark, from you to the part(s) that you're working with. Nothing in that equation involves earth ground except that other things that you're likely to touch might be grounded.
So when you're working on stuff, you don't really need to be earth grounded any more than when you're not working on stuff. You just need to be connected to the stuff that you're working on.
An ESD mat will be conductive enough that you can just set the case on it, put the strap on, and be sufficiently connected to the case. Then handle all the other parts by whatever it is that will eventually touch the case anyway, and you'll be fine. No need for earth ground in most cases, though it usually doesn't hurt either.
As a side note, I've built several PC's on carpet without any grounding at all just by handling parts as described above and by casually touching the case a lot. Never had any problems. But I'm also naturally paranoid enough in general to remember to do that.
Best Answer
Low-density foam is like styrofoam. You could compare it to a styrofoam cup or egg carton. Poking it with some IC legs will leave permanent holes. If bent, it will leave a permanent crease, though it's usually not quite as stiff as a styrofoam cup that can crack. If crushed (which it's quite resistant to), it will slowly return to some fraction of its original size. It's cheap and best for one-time uses, like shipping parts. Many cheap DIP ICs are shipped in bags with their legs stabbed into high-density foam.
High-density foam is like the padding in your tennis shoes. You might compare it to a carpet pad or even (on the extreme end of the spectrum) neoprene. Poking it with some IC legs will not leave noticeable holes. If bent, it will bend and spring back. If crushed (which can be easily done between your fingers), it will return to its original size almost instantly. It's expensive and best for long-term uses, like temporary storage of parts on a workbench or in a toolbox, or in a storage box for an assembled PCB. Using it for shipping parts gives your part a high-quality association; many of the more expensive parts I've purchased are mounted in plastic protective containers which surrounds two layers of high-density foam cushioning the part contained within.
With respect to the conductivity of that high-density foam; I wouldn't trust the comments of some random person on the internet. Techni Tool is a highly respected manufacturer. Their website claims that this foam has a resistance of 105 Ohms/square and dissipates static in <0.05 seconds. I'd believe that. This statistic was probably computed by a chemical engineer and verified by a test engineer with sophisticated equipment like 5-point surface resistance probes and ESD guns. When I read that comment from 'Breakout Ranger', I imagine an amateur in his basement with a $12.99 Harbor Freight multimeter poking some foam with the stock probes. Concerning? Not at all.