There are many possibilities, and they depend on:

(1) who takes advantage of the teacher's offer

(2) how many points those who do take advantage of the offer actually get back by doing so

For example, check out the attached pictures. The four variables here represent:

GRADE: roughly fits your description of original grade distribution.

NEWGRADE: the new distribution if everyone in class takes advantage of teacher's offer.

NEWGRADE2: the new distribution if only those who originally scored lower than the mean take advantage of the teacher's offer while everyone else doesn't.

NEWGRADE3: the new distribution if only those who originally scored higher than the mean take advantage of the teacher's offer while everyone else doesn't.

(All of these make the unrealistic simplifying assumption that each person who takes advantage of the teacher's offer manages to get back every possible point.)

As you can see, the standard deviation has substantially decreased in the first two scenarios, but increased in the third. As far as skew, the distribution (at least with these numbers I've made up) seems to get less skewed (more normal) in the first two scenarios, and severely less normal, essentially bimodal, in the third.

So it is impossible to say exactly what the teacher's offer will do to the grade distribution; it depends on the students' behavior. Speaking as someone who has taught, I would (sadly) not be surprised if NEWGRADE3 represents the most realistic of the three possibilities I've analyzed here.

As far as how you would fare in each of these distributions if each one was graded on a curve, calculate your z-score on each distribution.