Can't delete the people who do not belong. Do I just stop this tree and start a new one?
It's all one tree, so no, you can't do that, either.
In a shared, collaborative tree like this, there are many things you can't just outright delete, because that would irretrievably throw away someone's work. You can, however, edit nearly everything, and there's always a way to fix things.
Broadly, there are two correction methods: editing conclusions, and editing relationships. The former should only be used if the person is basically correct, but one or two conclusions are wrong -- someone made a typo in a year, or misread a name, for example. If it's the wrong person entirely, don't change the details to be someone else, change the incorrect relationships. If possible, put the person in the correct family, and before creating a new profile for the correct person, check if one already exists.
If you give us some details about the errors you've encountered, we can get more specific about how to fix it.
I am not sure why you have rejected the answer from @Julia Szent-Györgyi. She has given a very sensible answer. Her final line is, perhaps, the key. Tell us more about your problems and we will try to help.