I've been given as an exercise to show an encryption scheme that is CCA-secure but is not a secure message transmission scheme.
What is a message transmission scheme, and how does it differ from a regular encryption scheme?
An "encryption scheme" defines the encryption/decryption of data.
A "message transmission scheme" is about securing transmission and defines both "privacy" and "authenticity" between a sender and a receiver.
Since you haven't asked about the definition of CCA-secure (encryption) schemes and since you've been given this as an exercise, I won't mention anything about CCA-secure schemes because that would quickly provide an answer which would almost solve your exercise for you (and you wouldn't learn from that). But, when you keep in mind what I wrote above, you should be able to quickly come up with an encryption scheme that is CCA-secure while not being a secure transmission scheme.
Your CCA-secure scheme will be missing something a "message transmission scheme" provides… look closely at what I wrote, ask yourself what a "CCA-secure scheme" defines at a minimum, and then start thinking. You should be able to wrap your brain around it easily if you look at what each scheme defines.