The sentence can be broken down into three parts. The first part:
Innocence always calls mutely for protection[...]
This refers to the implicit call for protection that innocent things convey. They don't explicitly ask us for protection; we just intuitively strive to protect innocent things. This is why Greene refers to the call as "mute".
[...] when we would be so much wiser to guard ourselves against it[...]
"It" in this portion is referring to "innocence". Even though we have an innate desire to protect the innocent, Greene is telling us it would be wiser to guard against that innocence. He gives a reason in the third part of the sentence:
[...] innocence is like a dumb leper who has lost his bell, wandering the world, meaning no harm.
"Innocence" is accidentally harming the world in the same way a leper spreads leprosy. Greene's impression is that innocence isn't trying to harm things but that lack of intention does not reduce the harm being done.
Or, in other words, the innocent are destroying those around them without realizing it. This is why Greene is telling us to protect ourselves against innocence.
To fully understand the dangers that Greene is concerned about would require a full reading of The Quiet American and that would be out of scope for EL&U. Naturally, there are many who disagree with Greene and this view of innocence is not universally held.