Interestingly enough, the GMAT used to offer it when it was a paper-based test.

Rescoring Service
If there are any discrepancies between your self-scoring results and those on your score report, you may request that ETS rescore your answer sheet by submitting the appropriate fee and the form for this purpose your GMAT Examinee Score Interpretation Guide. But first check your answer sheet from incomplete erasures or light or partial marking, and check your calculations to be sure that they are accurate.

That's because the paper-based format was offered in the days when the GMAT was administered by ETS. I think ETS offers feedback for all its major tests (including the TOEFL). This has changed a few years ago (it was 2005 or 2006), when GMAC hired Pearson Vue instead. This is one of the major reasons why ETS is marketing the GRE as an alternative to the GMAT: they didn't compete in the past since it was also one of their tests, but now after being kicked by GMAC they have no incentive not to compete!