Message of condolences for a pet that has passed

你們好! I know a family who unfortunately had to say goodbye to their beloved young dog with a significant medical condition. I want to mail them a card to express my condolences, and would like some ideas on a sentence or two that I can write in Mandarin.

The family primarily speaks Mandarin, and while I was only able to communicate to a few of the members in English (which would then be translated by them to include the others in the conversation), I had told them that I studied Mandarin for 3 years in high school (though most of it is lost somewhere in the depths of my brain) and I occasionally tried to say some phrases I knew to help the non-English speakers feel included and seen. (Example: wishing them all a happy new year in their language.) So, while I plan to write most of the message in English, I think a little sentence or two in Mandarin would remind them that despite our language barrier there is still care and connection.

What are some appropriate ways to express condolences in Mandarin for this situation? And, culturally, is there anything I should avoid saying, even in English? Thank you all so much for your help!