“I'd love to, but I have a study group.”
This is a standard polite refusal pattern: show enthusiasm with I'd love to, explain the conflict after but, and offer another date such as How about Sunday? It softens the rejection.
A2-29 / CEFR A2 / EPISODE 29
Welcoming a friend with tea and cake
SceneAt Frank's home. Frank welcomes Tina with tea and a homemade cake.

WORDS & CONTEXT
This is a standard polite refusal pattern: show enthusiasm with I'd love to, explain the conflict after but, and offer another date such as How about Sunday? It softens the rejection.
Deal. is a short response confirming an agreement. Tina treats the arrangement for Sunday as a small, friendly bargain.
From the start means from the beginning, and a small thank-you means a modest gift of thanks. With the cake, Frank thanks Tina, who in A1-01 was not afraid of the stitches on his face and called him cool and special. It does not mean that Tina came to Earth in order to become his friend.
"Can the next cake be pink?" She is asking about the color of the cake, not the matcha. The small punchline is that Tina, moved by Frank's thoughtfulness, adds a request for her favorite pink as soon as the next visit is settled.