I've read the book as a child before, at least twice, but didn't then think deeper about it.
Am now re-reading it - and have read the first chapter showing the grey men convincing a potential "customer" to "save time".
He then proceeds to change his life according to all the suggestions he were given during the encounter, which he no longer remembers, thinking them his own thoughts.
Some thoughts, working with the analogy of the men in grey:
As Zadius Sky noted, it seems believing the lies is the means by which the people are sucked dry - the thing that "seals the deal".
And the things the people cut out of their lives makes their lives meaningless - not only without enjoyment, but also without creativity and learning. And in thinking a bit of the "message" of time representing life, I am struck by one thing in personal experience: The more I learn in a given "time", the "fuller" that time seems to me - in contrast, time in which I learn little seems "empty", as if it were indeed swallowed up.
Even if I remember little of a given time when I learned, there still remains a sensation of "fullness" in my memory - a feeling that the time was meaningful and indeed meant something. To be sure, time where I learn can also pass quickly - though often it simply feels as if I "have time" and things progress at just the "right" rate - and time where I don't can also pass slowly, if there's no distraction involved - but there always remains a difference in the "fullness" of it, looking back.
And if we really think of it, the things that really eat up our time are mainly the result of lies - to the degree to which they direct us, and as a result succeed in making our lives "empty" - just like junk food is "empty".
So the analogy is to me quite meaningful - when we believe in lies and live our lives accordingly, our "time" is rendered "dead" and sterile - in effect "eaten". And the battle is through us - what we do amounts to forces, creative or entropic, acting or manifesting through us - so such "eating" of our "time" indeed takes place on behalf of, or in "service" to, entropic forces.
And this might - at least to some extent - be a more tangible way for us to perceive a multi-level process of feeding, as believing in lies also amounts to the eating of one's energy of awareness.