Informally, a pushdown automaton has a way to store and use an infinite amount of memory (the stack). In a Turing machine, the only way to store an infinite amount of memory is to write it on the tape. But in a Turing machine without return, you cannot go back to the cells that you have already written, so that memory can never be used.
That means that a Turing machine without return cannot be “as powerful” as a pushdown automaton. The solution is a finite automaton.
If you want a more formal proof, you can start with the formal definition of a Turing machine without return, note that you can dismiss what you write on the tape (because you can’t go back), and construct a finite automaton that recognize the same language as the Turing machine.