First, its not a copyright infringement its Trademark infringement, they are different. Search the USPTO trademark data base to see his clients trademark and their filing date.

If you don't believe there would be significant you can do one of two things: 1) Have an attorney respond that upon reviewing his letter you have concluded there is no basis for infringement. 2) Ignore him (although watch your mail for a certified letter notifying you if they decide to file suit.)

If on the other hand you find they have a trademark, legally registered, and that your business is apt to cause their customers confusion, then you your response will be somewhat different.