The hugs from Alyssa come while they are all out together. The thank you note from Draco arrives later:
Ernie,
I believe Alyssa already made certain to thank you as properly as she can, but I cannot let it go without a proper note as well. Chatlin was quite confused by the bear, but made certain to wash it well, to Alys's delight.
Thank you for spending the day with us, and for making Alyssa's first birthday in London one she will remember.
Draco
[At the bottom of the note is a scrawl in green crayon that might, or might not, be the letter A.]