The words are very dissimilar in business (and most other contexts) 'eliminate' generally means to get rid of, or to remove 'rectify' generally means to repair or fix a problem 'close' generally means to finish or conclude. The businessman closed (concluded) the deal after rectifying ( fixing) his production problems and eliminating (getting rid of) his inefficient workers.

Eliminate means to remove or get rid of and rectify means to fix. Close as it relates to your example means to finish something. In the example you gave it seems like the comments are issues which should be fixed or as you put it rectified. You can also close an issue. I don't think eliminate fits what you are trying to say.

You could probably use any of them and people would know what you mean but there are slight differences in meaning between the three verbs. To close has several meanings. It's most common meaning is to close or block an opening (to close a door for example), but the meaning when used the in the way your sentence does, is "to bring to an end". A detective might close a case, for example. Note that 'to close' by itself doesn't really indicate whether the matter was successfully ended or not. To eliminate means to completely get rid of something (or somebody). You can eliminate a problem (something) , as well as eliminate a competitor (somebody). To rectify means to correct something or to put something right. That's presumably want you want the contractors to do to the issues you raise in your comments, You could also use the verb 'to correct'. I'll also add one small additional note on your sentence, It's really the issues described in your comments rather than your comments themselves that you want rectified, closed, or eliminated, I'd probably write the sentence something like this: Contractor is to rectify the issues raises in the comments.