As Bo Persson stated, if the message is the only problem in the post, editing this out would be too minor an edit.
I have seen edits in the past get rejected for removing thanks messages even though they did fix other things within the post such as capitilization, formatting etc. The combined edit fixed up the 2 or 3 things wrong with the post and there were no other improvements that could be made. Different reviewers seem to have different interpretations of the word minor so keep this in mind when suggesting edits.
You didn't mention signatures in your question but if you see any that contain links that lead to websites that have nothing to do with the answer, I would go ahead and edit out these links and the rest of the signature even if there is nothing else to improve upon within the answer. Make sure you mention that the link is unrelated to the answer and could be construed as spam in your edit reason. If there are other things to improve upon in these posts, then you should fix those issues also.