Perhaps in the fanfic, Harry teams up with the other students to stage a large - scale protest against Umbridge. Their united front and the chaos it causes might lead to the school board or the Ministry of Magic realizing that she is not fit to be in charge at Hogwarts. Or Harry could use his connections, like his friendship with Sirius or the Order of the Phoenix members. They could dig up some dirt on Umbridge from her past that makes it impossible for her to continue teaching at Hogwarts.
Often, Harry uses his intelligence and courage. He could find loopholes in Umbridge's rules and use them against her. For example, if she made a rule that was against the school's original code, Harry could prove it and get her in trouble. Another way is that he could get the support of the magical creatures at Hogwarts. If the centaurs or the house - elves had a problem with Umbridge, Harry could use that to his advantage to get her fired.
In certain fanfictions, Harry could get out of trouble with Umbridge through the power of truth - telling spells. He might be able to prove his innocence by using a spell that forces the truth to be revealed. Also, there could be instances where magical creatures come to his aid. For example, if he has befriended some of the magical creatures on the grounds, they could cause a commotion that diverts Umbridge's attention long enough for Harry to get away. Maybe a group of pixies start causing chaos in her office, and while she's trying to deal with them, Harry slips away unnoticed.
In some fanfictions, Harry might get Umbridge arrested by exposing her illegal and cruel actions towards students. For example, he could gather evidence of her misuse of power in punishing students with the blood - quill and present it to the proper authorities in the wizarding world.
Another way Harry could respond is with a sense of shock and disbelief at first. Given that Umbridge is supposed to be in a position of authority, Harry might be momentarily stunned that she would go to such lengths. However, his Gryffindor courage would soon kick in, and he would likely start to resist, perhaps by using his magic in creative ways to protect himself or to disarm Umbridge, all while trying to uphold the values of the wizarding world that oppose such cruel and unjust treatment.
In some fanfictions, Harry might use his powerful magic skills, like advanced spells he's learned secretly, to outwit Umbridge. For example, he could create a series of complex illusions that confuse her and lead her to leave Hogwarts on her own.
She's often portrayed as extremely cruel. She uses her position of power at Hogwarts to make Harry's life miserable. For example, she might give him excessive detentions with the blood - quill, just like in the original books. And she'll try to isolate him from his friends and undermine his credibility among the students and teachers.
The development of their relationship in Harry and Umbridge lemon fanfiction can be quite diverse. It could be that Umbridge, in an attempt to control Harry more closely, gets drawn into his world in a way she didn't expect. Harry, on the other hand, might start to see through her tough exterior and find some vulnerability in her. This discovery could lead to a series of exchanges between them, some filled with tension, some with a strange sort of understanding, and over time, this shapes their relationship in the fanfiction.
This could imply a lot of things. Fanfic is a realm of creativity where the normal boundaries of the original story can be bent. Harry liking Umbridge fanfic could be a sign of his growing maturity in the sense that he is willing to explore different perspectives, even of someone he dislikes in the original story. It might also be that the fanfic has a unique take on Umbridge, perhaps making her a more sympathetic character, and Harry is attracted to this new interpretation.
It reflects it by exaggerating the already existing tension between Umbridge and Harry. In the original story, Umbridge was a very strict and unjust authority figure towards Harry. The fanfic just takes it further. For example, the cruel punishments she gives Harry in the books are made even more extreme in the fanfic.
In some fanfictions, Harry might outsmart Umbridge by using his knowledge of magic in unexpected ways. For example, he could use spells that are not commonly known to get around her rules. Maybe he uses a charm to make her quill write false reports, thus confusing her when she tries to use those reports against him.