Is it appropriate to mail a thank you card following the rejection of a job offer?

Even though your GM has a few months to live, you can see her after work, you still have to work. Thats no excuse not to take the job.

In today's market, you'd be a fool to reject the offer. I doubt your grandmother would want you to either. I understand you wanting to spend time with her, but you shouldn't sacrifice your future to do so. Rather than outright rejecting the offer, could they wait a month or two for you to come? Work a 4 day week so you could visit on weekends?

All you have to do say in a note is;

Dear Sir / Madam (if you know their name use it)
Thank you for the opportunity of interviewing with you on _____ (date and time). It would be an amazing opportunity for me to work with you. Unfortunately I'm going to have to reject your offer at this time.

Sincerely,
Your signature
Your name

Don't get too personal, they don't need to know what's going on in your life right now.

I don't see a problem with it. Might help if you want to work for the company at some point in the future.

You are better off calling or emailing. A letter in the mail isn't ideal these days.

entirely up to you, but you'd be wasting your time if you send it, the company is not interested in mail from quitters

They hired you for their own benefit because you were the best applicant.for the a job, not to do you a favour so what, exactly would you be thanking them for.

No one gives two shiits about a thank you card for a job offer.

The only thing the company cares about is hiring someone to do the stuff that needs doing.

It wasn't a favor/gift that you got the job interview. It wasn't a favor/gift you got the job.

If you aren't taking the job, just don't take it. There is nothing to give thanks for.

Honestly, if I got a "thank you card" from someone who declined to take a position I'd be thinking "thank God I dodged that weirdo."