Edit: Thanks to Ian's score guide below, I was able to figure out all 3 star score prizes. For 2 star score prizes, it's the previous level 3 star prize.

Post what levels/score give you what prizes. I'll update this post as we get new prize info.

Level 1, 3 stars: Green Xoi Paw
Level 2, 2 stars: Milky Coffee
Level 2, 3 stars: Sushi Shuffle
Level 3, 3 stars: Extra Milky Coffee
Level 4, 3 stars: Red Xoi Paw
Level 5, 3 stars: Heartfelt Hymns
Level 6, 3 stars: Xoi Candy Dispenser
Level 7, 3 stars: Sushi Masters
Level 8, 3 stars: Yellow Xoi Paw
Level 9, 3 stars: Banana Tattoo
Level 10, 3 stars: Wok
Level 11, 3 stars: Xoi Puppet
Level 12, 3 stars: Knork
Level 13, 3 stars: Ramen Tattoo
Level 14, 3 stars: Mint Tea
Level 15, 3 stars: Farley Biscuit
Level 16, 3 stars: Snow Xoi
Level 17, 3 stars: Pineapple Tattoo
Level 18, 3 stars: Carrot Flute
Level 19, 3 stars: Bread Basket
Level 20, 3 stars: Lotus Tea
Level 21, 3 stars: Old Spell
Level 22, 3 stars: Buffet Shirt
Level 23, 2 stars: Old Spell
Level 23, 3 stars: Gingerbread Buffet Restaurant
Level 24, 3 stars: Musical Chair
Level 25, 3 stars: Buffet Eye Make Up