Bounded-symbol conjecture for truncated Toeplitz operators

Let $\Theta$ be an inner function. A bounded-symbol conjecture asserts that any bounded truncated Toeplitz operator has a bounded symbol if and only if $\Theta$ belongs to $(CLS)$. This conjecture connects the bounded-symbol problem for truncated Toeplitz operators with the class $(CLS)$; the supplied text gives no resolution, so its status is left open.