I don't understand why you'd want them to built another CI system. Just for the sake of it?
Feels like using a free Jenkins gets you everything you want. Doesn't need more than a container or Java either.
That's also perfectly fine if that's what it is. I would just phrase that as "They don't have CI but they provide hooks."
That's also perfectly fine if that's what it is. I would just phrase that as "They don't have CI but they provide hooks."