Kim–Lim–Lovejoy congruence conjecture for the mock theta function A(q)

Let $N_A(n)$ be defined by

$$A(q)=\sum_{n=0}^{\infty}N_A(n)q^n.$$

Let $p\not\equiv7\pmod8$ be an odd prime, let $\delta_p$ satisfy

$$8\delta_p\equiv1\pmod{p^2},$$

and let $k,n\in\mathbb Z$ with $\left(\frac{k}{p}\right)=1$. Kim–Lim–Lovejoy's $A(q)$ congruence conjecture. Then

$$N_A\bigl(p^2n+(pk+1)\delta_p\bigr)\equiv0\pmod4.$$

This is a mod $4$ congruence for coefficients of the second-order mock theta function $A(q)$. The paper states the conjecture in connection with the odd-balanced unimodal sequence generating function, but the supplied text gives no explicit resolution status.