What type of behaviour is showing, but withholding, a reward?
The problem is that this doesn't fall under any of these conditioning definitions in behaviourism because the store isn't really trying to condition a response.  They're just trying to get you to do one thing once.  The behavioural techniques you mention are designed so that you get an organism to make a conditioned response spontaneously whenever the conditioned stimulus occurs (or is anticipated to occur or a second order associate occurs.. ok, it's more complicated than that).  

It's also not really considered conditioning when it's done through insight.

That doesn't mean there's no science behind this.  There's lots and it falls more under behavioural economics than psychology, unfortunately.  (Consumer psychology hasn't really moved to be as complementary to behavioural economics as it probably should be.)

That said, these kinds of "nags" would be closest to negative reinforcement.  They're encouraging a behaviour that removes an aversive stimulus... being reminded of a gain you did not receive.  Punishment is typically more to extinguish a behaviour.  They certainly don't want you to stop shopping.  Sometimes it's hard to see what it is until you figure out the goal behaviour.

(As an aside, what they want more than anything is your personal information.  That's what they're trying to get.)