Church-Turing thesis is a dualism
There's another possibility: hypercomputation is not implementable in the real world, and is only an imaginary/theoretical concept.  If this is the case, then there is no contradiction with the Church-Turing thesis.

Of course, anyone can invent imaginary worlds where strange things are true.  For instance, there's the computer scientist's Superman: not only can he leap tall buildings in a single bound, he can also solve undecidable problems in his head!  I suppose one could imagine such a thing, but that doesn't mean it has any correspondence to the real world, and the possibility of imagining such a Superman doesn't contradict the Church-Turing thesis.  The study of hypercomputation can be thought of as asking, well, ok, so Superman might not be real, but what if he were?

The Church-Turing thesis is a hypothesis about the real world, so imaginary schemes that can't be implemented in the real world don't contradict it.