What does Lewis mean by the things that stifle bitter resentment in elders in A Grief Observed

Lesley's answer goes into some good depth about the book as a whole. I wanted to offer my own thoughts, based on a more 'local' context for the quoted paragraph.

Leading in to the quote (as Lesley noted), Lewis was in the early stages of grief and feeling as though God had abandoned him -- no response to his prayers, no comfort, no nothing. The paragraph immediately before the one you quoted in the OP (and immediately after the one Lesley quoted) reads,

Not that I am (I think) in much danger of ceasing to believe in God. The real danger is of coming to believe such dreadful things about Him. The conclusion I dread is not 'So there's no God after all,' but 'So this is what God's really like. Deceive yourself no longer.'

Lewis seemed to be detecting the 'early warning signs' of anger and resentment toward God. He could easily envision the agonizing grief and sense of abandonment turning into a loss of faith in God's essential goodness... which, in turn, would lead him to bitterness, maybe even an ultimate rejection of his Lord. The idea that things could be going that direction (quite justly) frightened him.

This led him to ponder the lot of "our elders," the saints of biblical times. Did they perhaps start down that same dangerous road he saw before himself? Were their unswerving expressions of faith, "Thy will be done," sincere and heartfelt, or merely a front? Either way, since they didn't abandon their relationship with God, how did they deal with those awful feelings?

• "stifled through sheer terror": the terror of a permanently broken relationship with God, and the doom that implied. (Note: Lewis was not a believer in the doctrine of eternal security.)

• "an act of love": clinging to what love they still felt for God, by putting up a brave and faithful front. (Today we'd describe it as "Fake it 'til you make it.")

• "hide the operation": concealing those same conflicted, wrenching feelings they were wrestling with -- the 'operation' being the act of 'stifling' those dangerous emotions.

Or to sum it up, Lewis (I believe) was speculating on whether the 'elders' he refers to, might have experienced the following sequence of events:

1. Faced with an overwhelming trial or loss
2. Sensed (as Lewis himself did) the beginnings of resentment toward God
3. Immediately terrified at where that resentment might lead
4. Drew on their remaining love to give an outward display of submission, to finish stifling the resentment while keeping the whole mess of conflicted emotions hidden from others

Section One deals with Lewis’s initial reaction to the death of his wife. He asks this about God:

Why is He so present a commander in our time of prosperity and so very absent a help in time of trouble? I tried to put some of these thoughts to C. this afternoon. He reminded me that the same thing seems to have happened to Christ: “Why hast thou forsaken me?” I know. Does that make it easier to understand?”

Then comes the quote about “our elders” who submitted to God’s will and the question of bitter resentment being stifled, the whole thing “an act – put on to hide the operation” (page 8).

Further on in the book, in Section Two (page 29), Lewis likens grief to fear, suspense or waiting for something to happen. It is in Section Three (page 45) where Lewis uses the metaphor of an amputation to describe how one never really recovers from the grief of the death of a loved one.

To say the patient is getting over it after an operation for appendicitis is one thing; after he’s had his leg off it is quite another... Presently he’ll get back his strength and be able to stump about on his wooden leg. He has ‘got over it’. But he will probably have recurrent pains in the stump all his life... he will always be a one-legged man.

In Section Four Lewis realises that he is going through a process and likens it to a winding valley where any bend may reveal a totally new landscape. He then introduces another metaphor to describe the process he is going through:

Two widely different convictions press more and more on my mind. One is that the Eternal Vet is even more inexorable and the possible operations even more painful than our severest imaginings can forbode. But the other, that ‘all shall be well, and all shall be well, and all manner of things shall be well’.

Lewis is moving through the process of grief, which is not unlike recovering from an operation. He likens the death of a beloved to an amputation.

Perhaps now we can understand the reference to “the operation” given on page 8. It is a metaphor that covers all sorts of suffering, and how Christians who came before, (“the elders”) the biblical saints, who submitted to the will of God and were persecuted and suffered for righteousness’ sake, struggled with internal doubts, resentment and fear. “Why, God, are you allowing these terrible things to happen to me?” The “operation” may be a reference to the price they pay for submitting to God’s will, just as Christ Jesus, who paid the ultimate price, suffered in order to do the will of his Father in heaven.

It is human nature to question and challenge what appears to be unfair, or unreasonable, or wrong. This is where resentment is stifled and it may look to others that the believer who is suffering is simply putting on an act. Just like grieving after the death of a loved one, all sorts of internal struggles are besetting other believers who did not fully understand why these dreadful things were happening to them (“the operation”) but who, nevertheless, endured. You may find this article helpful: https://en.wikipedia.org/wiki/A_Grief_Observed