You are right to say that it is not a complete sentence but it does have a verb. 'strick' is the verb in the clause. To make it a complete sentence, you can change 'for expressing' to 'expresses'.
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Hongkie We normally use 'among' instead of 'between' when we talk about more than two things.Hi Hongkie,
The card expresses your heartfelt feelings in a way that strikes the right balance among adorable, sincere and tasteful.