Is The Handmaid's Tale utimately a feminist work of literature, or does it offer a critique of feminism?
You can argue either way on this one. Offred does mention a couple times in the novel that the society that they have is all a result of a freakishly overdone attempt to respect women and give them their rights back. It does go a bit astray, but at least women are respected, protected, and not treated like mere objects to satisfy one's desire. Since feminism advocates female power and the ultimate respect of women, this awful society could be seen as an extreme case of that; in that sense, it is a critique. The torture and killing of any male that does go against the strict moral codes towards women also is an extreme and twisted offset of giving women the respect they deserve.
However, if you want to look at it from the other angle, there is evidence to support and argue that it is a feminist work. In the beginning, before the takeover of the Gilead society, women were constantly violated, brutalized, raped and disrespected--this was not good, and pointed out frequently in the novel. That is a travesty that the feminist movement fights against. Also, bevore, men held the power, and in the Gilead society, men still held the power. Women were used as pawns either for breeding or for hard labor. It was a tricky sort of subversion though; men too were condemned and tortured, and women were supposedly given more respect and power. Offred sees through this though, and realizes how little freedom they actually have, and the only power that they do have is through their bodies, which are hidden and repressed to the point of driving both males and females insane. In trying to control the power of sexuality in the female body, they only made it even more powerful and dangerous for men. This suppression of female nature and beauty is anti-feminist, and what their society was about. The fact that women couldn't read and held no true positions of power also supports the idea that this was a feminist work.
I hope that those thoughts help to get you started; good luck!