Interesting question; the soil may be depleted, so when refilling, maybe consider fresh soil. Before refilling the hole, place a thin vertical solid plastic barrier material around the perimeter of the excavated hole to stop/slow incursion of new roots, that extends down deeper than the bottom of the hole. The hole would have to be deep enough to discourage vertical upsprouts of ivy from remaining roots. A barrier on the bottom of the hole might also be beneficial.
Would suggest Not using any artificial spray etc on the ivy roots: doing so would make the hole unsafe to work in & around, it might eventually get into the water supply, it might ruin the ivy extending up the walls, which would then need to be removed, and would leave an unsightly gap in the live ivy growth on the wall. For a long while nothing would grow well in the hole, and if it finally did, it would be unsafe to handle or to tend.