I am not sure what kind of a reply you are expecting. There are certainly several possibilities, none of which, however, can be fully satisfying in a purely philosophical sense.

As a philosophic-scientifical naturalist, I hold that, indeed, there are no such things as minds, and that, therefore, the question itself can be sensibly asked sementically, but is otherwise empty because it derives from ontologically false premisses. The statement that there be no such things as minds needs qualification. It contends, first, that there be no single, undivided, esoterical (i.e. non-physical) entities constitutional of human cognition and emotion to which the term 'mind' correctly applies. As concerns my personal stance, it further claims that there be no single, undivided, physical entities constitutional of human cognition and emotion to which the term 'mind' correctly applies. Instead, there are brain processes occuring in and among regions of the brain, while there being no single centre where all processes meet. Thus, from a natural point of view, David Hume's conclusion that, since one cannot detect a self, or ego, by introspection, there in fact is no such thing ontologically would be true in an even stronger sense than Hume himself would have thought.

A more philosophical, though perhaps similar in its consequences, objection to the proposition that everything there be ontologically depend on a mind perceiving it is that it is not true that our observations accommodate both a materialist and an idealist position equally in an unprejudiced sense. That is to say, idealism both overintellectualizes perceptual observation and conflates biased or prejudiced presuppositions with it.

On the other hand, from a purely philosophical standpoint, the idealist may simply respond by pointing out that the same charge apply to the materialist position. And this is what I meant when I wrote that there be no fully satisfying answer to the question posed in exclusively philosophical terms.

Besides, I disagree with your assertion that '[t]he quote itself grants that there is a world exterior to the human mind that is either perceiving it, and this over looks the problem of an external world.' On my reading, the quote you initially gave entails exactly the question you charge it to overlook. Both positions, to be sure, need to assert this, albeit in different manners, yet it is a presupposition, not an explicitly argued proposition, to both, so that either a response to it can legitimately be demanded from both or be skipped for the sake of argument, as is done so often in philosophy, since asking each question that can principally be asked would necessitate any discussion to start from scratch, leading nowhere.