Year eight pupils at Bridlington School were asked to "imagine that you are a parent of one of the Manchester bombing victims. Write a response to the point of view that "All terrorists should be forgiven."
Screenshots sent to The Yorkshire Post of the homework app, Show My Homework, suggest it was set for a PSHE lesson.
A parent of a 12-year-old pupil at the school first saw the homework being circulated on social media and believed it was a "hoax."
She said she was "shocked" when she checked her daughter's homework app and saw it had been set on December 16.
The mum-of-four said: "I I honestly didn't believe it. I thought it must be a hoax. I thought someone must have made it as a prank on the teacher.
"I was just in complete shock. It's just wrong. I normally can't fault the school but how could the teacher think this is appropriate? It's not normal."
She added: "My daughter is quite tough but she said she can't bear to think about how the parents feel. It's hard for anyone to imagine that - especially 11 and 12-year-olds.
"It happened so recently. I remember my daughter even wanted to go to the concert but we couldn't get tickets.
"There are children at the school who went to the concert or who have been affected by it. It was only two years ago. It is still so raw.
"As parents, we are trying to protect our children but this homework will cause them significant emotional harm.
"My daughter certainly won't be spending her Christmas doing this homework."
Another mother with two children at the school said: "I think it is disgusting and morally wrong.
"A lot of parents have emailed the school and are waiting for a response. We are all disgusted and upset that this has been set as a homework
"I am 39 years old and could never comprehend losing a child, especially in such a horrific way, never mind then thinking about forgiving the terrorist.
"How on earth did this teacher think this was appropriate?"
In total, 23 people died at the terror attack at the Manchester Arena in May 2017 when Salman Ramadan Abedi detonated a suicide bomb after a Ariana Grande concert, while 139 were wounded. More than half of the injured were children.
Bridlington School headteacher Kate Parker-Randall said: “Firstly I would like to apologise for any upset that this piece of work may have caused.
"The essay was set as part of a personal, social, health and economic education (PSHE) lesson which was considering the consequences of crime and the aims of different punishments.
"It followed a discussion in class about a newspaper report that the mother of one of the victims of the Manchester Arena attack had forgiven the bomber for killing her son.
"The essay was intended to allow students to formulate their own views about whether hate or forgiveness are the best response to even such terrible crimes.
"I would like to reassure parents, pupils and the community that the feelings aired on social media were totally unintentional consequences of setting this homework, however, I do understand that some people may find it difficult to understand why a school would ask students such a challenging question.
"It is important that students should be able to express their own thoughts and give reasons for their feelings.
"However, having reflected on the matter we would in hindsight have posed the homework question in a different way.”