This is a tricky question. The option I would most like to see listed is rejected, because ignored seems too passive and betrayed too active. Rejected has many uses, from the neutral and professional rejected proposal to the personal and emotionally-charged to feel rejected. I think this ambiguity is part of what makes rejected an apt answer when given little context.
medica presents a compelling case for ignored. And Third News observes that "when they most needed him" emphasizes the dependence of the supplicants on the party who refuses to help, giving a sense of implicit (or previously established) obligation whose terms have been breached; it seems fair to me to call this betrayal. I would like to suggest that betrayal too, even without "when they most needed him," is an acceptable answer.
The first example of the phrase in popular use that came to mind is from Disney's "The Lion King":
Timon: Look, kid. Bad things happen, and you can't do anything about it. Right?
Young Simba: Right.
Timon: Wrong! When the world turns its back on you, you turn your back on the world.
Some background: Simba is a young lion who runs away from his pride (or herd), because he holds himself responsible for the death of his father, the king and leader of the pride. Timon and Pumbaa (a meerkat and warthog) are self-described outcasts who find Simba and invite him to join their group when they learn he is running from his past. Timon uses the above quote to persuade him to do so.
In explaining what he means by this, Timon starts the song Hakuna Matata, which reveals Pumbaa's story:
[Pumbaa] found his aroma lacked a certain appeal
He could clear the Savannah after every meal
I'm a sensitive soul, though I seem thick-skinned
And it hurt that my friends never stood downwind
And oh, the shame, he was ashamed
Thoughta changin' my name, oh, what's in a name?
And I got downhearted, how did you feel?...
While there are cases for being ignored in Pumbaa's (neighbors ignored or eschewed him because of his aroma) and Simba's (fears of his pride ignoring his insistence that he didn't mean for his father to die) scenarios, I feel the ones for betrayal are good too.
If we assume sensitive soul Pumbaa (who is kind throughout the film) made a point of accepting his friends despite their faults, then it is easy to see how Pumbaa might feel betrayed: His friends could not bring themselves to even pretend (for Pumbaa's sake) that his odor was a non-issue, that they valued his company more than their comfort.
Timon is suggesting that Simba feels victim to a similar bum wrap, that Simba's world (his herd) will offer neither forgiveness nor reprieve for his mistake, perhaps thinking that Simba did it intentionally in order to become king himself. To see the betrayal in this situation, consider M-W's definition of betray:
3: to fail or desert especially in time of need: betrayed his family
How can Simba be a member of the pride, let alone its leader, if fellow members entertain such suspicions about him? To be an equal, he needs them to accept his pleas of innocence as true.
Timon's response? Betray them back. Desert them like they deserted you. This is what Timon, Pumbaa, and Simba kind of do when they run away and become a tribe of their own.
From the same MW link, to betray means:
to hurt (someone who trusts you, such as a friend or relative) by not giving help or by doing something morally wrong
While the quote doesn't say that the supplicants were hurt, it does say that they were in need and that help was refused. TFD cites The American Heritage® Dictionary of the English Language, Fourth Edition when it defines "turn (one's) back on" as:
turn (one's) back on
To deny; reject.
To abandon; forsake.
The words abandon and forsake are in Thesaurus.com's top picks for synonyms for betray.
In the end, I think given the situation answers C and D are equally justifiable. Without an answer key, I would resort to chance in choosing an answer.