letter of thanks; acknowledgment note
A written note or letter sent to express thanks or acknowledge something received; more formal and written-sounding than お礼の手紙.
I received a gift, so I wrote a thank-you letter right away.
Please don't forget to send a thank-you note to the teacher.
I wrote a thank-you letter to the teacher who had helped me.
I sent a letter of thanks to the client.
Last week I received a thank-you letter from a customer.