When writing to a third party, clearly state that you are conveying your client's position or understanding, rather than your own.
You are entitled to accept at face value what your client tells you, unless you know it is false. To avoid a complaint, ensure that the third party knows you are not making your own accusations or stating your personal views.
You should always respond to a complaint, even from third parties. But be aware that your duty to respond does not override the duty of client confidentiality and legal professional privilege. Explain to third parties that a full response to all of the issues they have raised might not be possible due to client confidentiality, unless your client consents to release the information.
Although you may need to treat these types of complaints differently to a complaint from your own client, don't ignore them. Not responding to a third party could, of itself, result in a further complaint.