Homotopy ribbon-slice conjecture

Let $K$ be a knot in $S^3$. It is homotopy ribbon if there is a slicing disc $\Delta$ in $D^4$ such that the inclusion induces an epimorphism

$$\pi_1(S^3\smallsetminus K)\twoheadrightarrow \pi_1(D^4\smallsetminus\Delta).$$

Homotopy ribbon-slice conjecture. A knot is slice if and only if it is homotopy ribbon.

This is the topological-category version of the ribbon-slice problem. The statement is presented as an open question in the paper and is related to the distinction between topologically slice and smoothly slice knots.