Hallmark cards tend to leave a lot of blank space to write. It’s absolutely genuine when you grab a pen and start writing. Bonus points if the Hallmark message is relevant to the person receiving it and maybe something you can riff on in the handwritten part. Funny cards are also great!
So I would say the golden rule continues to apply: the more effort is visible, the more genuine it is.
(and no, it's not genuine)