How to resolve 'Server responded with an error' on iPad after potential hack?

My mother got a login verification notice on her phone (actually, at least four or five). The verification notice stated they were from a town about 23 miles away. Thankfully, she did not allow any of them. She called my sister, who helped her change her password and log back in on her phone. They didn't think about the iPad. When she later tried to log onto her iPad, she also got a verification message, but it listed the same nearby town. Out of an abundance of caution, she did not allow this either. Based on an Apple support post, she then restarted her iPad, but now she gets an error message. Any ideas?

[Re-Titled by Moderator]