Litherland's radical conjecture for quadratic quandle invariants

Let $K$ be a link. Let $A_p(K)$ be its Alexander module, let $A'_p(K)$ be the submodule of elements annihilated by $h$, and let $\operatorname{Rep}'(K,\mathbb{E}_p)$ be the annihilator of $A'_p(K)$ inside $\operatorname{Rep}(K,\mathbb{E}_p)$. Let $\eta$ be the symmetric bilinear form on $\operatorname{Rep}(K,\mathbb{E}_p)$. Litherland's radical conjecture.

$$\operatorname{rad}\eta=\operatorname{Rep}'(K,\mathbb{E}_p).$$

The claim is presented as a stronger statement following the rank conjecture, whose context describes the preceding equality as verified only in finite computational cases. No general proof or disproof is given.