Most clients should care about code that is long term maintainable even if it isn't in the contract. Thus tests are good. As a professional engineer (I'm intentionally invoking professional in context of other industries where the term has legal implications on quality, even though it doesn't exist for software it should!) you should care about that
If it is in the contract and specs (either way) then you do what you are paid to do.
Caring about the client's opinions re: unit tests is a little like caring about their opinion re: the interior color of your vehicle. Sure we can talk about it if it comes up over a beer some Friday evening but we're certainly not going to change anything based on the conversation.