How to fix the assistive touch on my iPad?

That sounds like the Accessibility Shortcut. You can turn it off by triple-clicking the top button. You can also control what it does by going to Settings/Accessibility/Accessibility Shortcut.

For those who stumble onto this chat because their virtual button has disappeared. I just found out from Apple Support Assistive Touch virtual home button does not work (disappears) with ”Accessability - Display & Text Size -  Bold Text” turned on. Turning this off and my virtual button comes back.

Mine does not do that

If you would like to see yours do that go to Settings/Accessibility/Touch/Assistive Touch and turn it on.

Thanks for that update!