Looijenga's conjecture on the smooth Torelli group of Enriques surfaces

Let $Y$ be an Enriques surface, and let $H^*(Y,\mathbb{Z})$ be its integral cohomology equipped with the quadratic form $Q_Y$. Define the smooth Torelli group by

$$\mathcal{I}_Y:=\ker\bigl(\operatorname{Mod}(Y)\to\operatorname{Aut}(H^*(Y,\mathbb{Z}),Q_Y)\bigr).$$

Looijenga's conjecture. The smooth Torelli group is trivial:

$$\mathcal{I}_Y=\{1\}.$$

The conjecture concerns whether every mapping class of an Enriques surface that acts trivially on integral cohomology is itself trivial. It was suggested by Looijenga; the supplied source does not state whether it has been resolved.