Here is an only somewhat facetious remark about gratuitous evils that I have not seen mentioned in discussions on the problem of evil (maybe because it’s so bad? but if it is, I don’t see why).
A gratuitous evil is an evil for which there is no outweighing good—an evil that serves no ultimate purpose, and so is unnecessary. But for any gratuitous evil you pick (or even gratuitous evil as a category), it seems at least possible that the act of discussing or thinking about it renders it non-gratuitous. For the very discussion about whether some evil is gratuitous may serve as an outweighing good of some kind (perhaps deepening one’s philosophical or existential grip of reality, or one’s understanding of God and his ways).
If so, the only way evil could be gratuitous would be if no one thought about it at all. But if no one thought about it at all, it could never serve as a defeater for the rationality of belief in God. One cannot think about gratuitous evil as a defeater for belief in God without thereby generating a defeater for the belief that there are gratuitous evils. Thus, it would not be possible to rationally believe there are gratuitous evils, even if there were such.