That’s a thoughtful gesture but may be misunderstood like Gian said. I think saying you are sorry for their loss and just listening if they want to talk about it may be best.
I'll take a dog over a human any day all day. What I wont do is acknowledge some roasties who is channeling her maternal instinct through her fur baby.
Unfortunately, too dark. They won’t get it. Send something sentimental like this: