If Harry Potter gets the Dark Mark in fanfiction, it would completely change his relationship with the wizarding world. He'd be instantly seen as a Death Eater, and his friends would be in a state of shock and confusion. His standing at Hogwarts would be in jeopardy, and he'd likely be hunted by the Order of the Phoenix as well as the Ministry, at least until they figure out the truth.
In addition to the above, other characters from the wizarding world could be involved. For example, the Order of the Phoenix members. They might be suspicious of Harry at first but then come to his aid. And there could be some new characters created specifically for the fanfiction. Maybe a mysterious old wizard who has knowledge about the Dark Mark that no one else does and helps Harry on his journey to rid himself of it or at least understand it better.
In some versions, Harry might struggle with the internal conflict of having the Dark Mark. He could face discrimination from those who believe he has truly turned to the dark side. This could lead to a situation where he has to prove his innocence while also dealing with the newfound power or connection that the Dark Mark might bring.
One consequence could be that the Death Eaters no longer sense his connection to Voldemort. This gives Harry an advantage in his fight against them as they can't track him through the Mark.
In some fanfictions, Harry might use powerful ancient magic that he discovers in a hidden library or from an old wizard. This magic could be specifically designed to counter the dark magic of the Dark Mark.
It could change the way the wizarding world views Snape. Since the Dark Mark is a symbol of his connection to the Death Eaters, its removal might make people see him as a redeemed figure. For example, the students at Hogwarts who once feared him might start to respect him more. And the Order of the Phoenix members might trust him even more fully.
Perhaps Harry uses some powerful ancient magic he discovers. Maybe he finds a spell in a long - forgotten book in the Room of Requirement that has the power to break dark enchantments like the Dark Mark.
Well, if Harry has the Dark Mark in fanfiction, it would completely change his relationship with the wizarding world. He'd likely be seen as a threat and be shunned. His friends might turn against him out of fear or be forced to by the Ministry. It would also make his fight against Voldemort much more complex as he'd be associated with the Death Eaters.
The plot would change drastically. Firstly, Harry would lose the trust of many. Dumbledore might be more suspicious of him. Secondly, the Death Eaters could have different plans for him. They might try to use him as a weapon against the Order. Thirdly, Harry would have to constantly hide the mark, adding a new layer of secrecy to the story.
Some of the die - hard Death Eaters could also be antagonists. They might not trust Harry even with the Dark Mark and try to undermine him or expose his true intentions if they suspect he's not truly on their side. Bellatrix Lestrange, for example, is so fanatical about Voldemort that she would be a likely candidate to oppose Harry even if he seems to be part of the 'dark' group.