You have two ways you can do this, depending on whether or not you want to make the board public. Both make use of the comments setting found under the board profile.
If you make the board public, you can select "public" under comments in order to allow anyone with a Trello account to leave a comment.
If you don't want to make the board public, you can create a new organization for members of your team and members of your client's team and associate the board with that new organization. Then you can select "organization" under comments in order to allow anyone in the organization to leave a comment.
As a bonus, you can do the exact same thing with voting.