How do the committees think of an international student who is exempt from the English admission requirement(TOEFL) but has poor GRE verbal score?
If you meet the requirements of a TOEFL waiver it would be a waste of your time to take this test. I would only worry about the GRE score if there is some sort of minimum admission score for the school you are applying too. 

It's better to make sure that your statement of purpose is written in excellent English and that you provide other evidence of academic and research potential. Committees are used to dealing with international students and the challenges of English.