Should you write a thank you note for a thank you gift?

Answer 1

It is polite to recognize any gift with an acknowledgement.

However, the acknowledgement need not always be a note. Depending on the situation, sometimes a personal thank-you, or a thank-you by phone or e-mail may be appropriate.

What matters is that the giver of the gift knows that you received it, understood the intention behind why they gave it, (hopefully) that you appreciate the gift and will use it appropriately (so they are reassured that they chose your gift well), and through all of this that the social bonds between you are strengthened.

All that having been said, everyone likes getting a sweet note, because it is something you can keep to remind you of a kind person and the friendship you share with them.