Why is 'Grudger' an evolutionary stable strategy?
Unfortunately it is not necessary to invoke group selection to answer this question.  This is one of the reasons that Dawkins likes this discussion so much - he does not believe in group selection and so the discussion in SG does not invoke group selection.  ESSs are described in the book as the product of direct competition or interaction between genes. 

ESSs in this case, can be described in terms of game theory.  In the famous Prisoner's Dilemma experiment, Grudger is similar to tit for tat, which 'won' the competition in the original Axelrod contest.  

To see how this works you make a simple win/loss game matrix:  

     G        NG
G    win 1    win 3
NG   lose 3   lose 1


if you are groomed you win 1, if you are groomed, but you don't have to groom - even better win 3 (say)
If you groom but are not groomed, lose 3
If neither of you are groomed, you both lose 1

one might argue the exact proportions, but the point is that getting some thing for nothing is better than reciprocating, and getting nothing for your efforts and time are a loss, because you could have been getting groomed by someone else. As you can see cheaters end up in the top row all the time.  grudgers end up along the diagonal, and once in a while in the lower left, Suckers get stuck in the lower left a lot whenever there is a cheater around. 

now run this encounter over and over.  A behavior which scores negative the more times you run is not stable - they are going to disappear from the population, at least if this disadvantage is real

It has more than one stable outcomes in populations, a population that is full of Grudgers will all groom each other as before you know everyone, you assume they will reciprocate.  Everyone wins!

Any invading Cheaters will quickly be at a disadvantage, in that they will not be groomed more than N times where N is the number of grudgers in the community.  Note that there is an equilibrium here - the Cheaters may exist in a small number - when N is large enough for a cheater to get enough grooming to make a 'living'.  

Suckers can also exist within a population of grudgers, but a population of Suckers where Cheaters show up are quickly sucked dry by the cheaters over several generations where you tally up 'points' and give more, healthier offspring to high scorers.  They are not ESS stable.  

Cheaters are also stable - nobody ever wins, but they don't lose big either and any invading grudgers can't get groomed.