How do the committees think of an international student who is exempt from the English admission requirement(TOEFL) but has poor GRE verbal score? I am planing to apply for Ph.D programs in Mathematics in U.S.

Since I have studied in U.S. for two years and eligible for TOEFL waivers according to the websites of many math departments, I don't have to retake TOEFL in order to apply. But my GRE verbal score is between 150 and 155, which is less than many applicants who have never studied in English-speaking countries.

I wonder how do the committees think of my case when I don't send my TOEFL scores to the school? Can I increase my chances of being accepted by sending my good TOEFL scores(say 100+) to the math departments which don't require TOEFL scores for my case? Or the committees simply ignore the TOFEL scores sent to them when they know the applicant doesn't have to send them?
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.