1. Write on the memo line of the check "accord and satisfaction", if he cashes the check, that means he is satisfied.
https://en.wikipedia.org/wiki/Accord_and_satisfaction
2.
Dear XXX,
Thanks for your response on XX/XX date. It is unfortunate that my earlier communication cause your grief. But I think you are overreacting.
My concern remains to be, in your estimate you made clear the fees are charged for time spend on the job. You did not mention the time commuting to work site will be charged. I am happy and willing to pay what I agreed to, $50 for the hour acutally worked. But I am not ready to pay something I never agreed to.
As for your comments about Asians, they are over the line and unprofessional. I don't know any business owner can succeed by insulting their customers. The comment destroyed the good will you established on your first visit and made it difficult for me see reason to your side of the dispute.
Enclosed is a check of $50 for accord and satisfaction.