jquery.unobtrusive-ajax.js is a Microsoft library for supporting @Ajax.* helpers, this is a plugin that unobtrusively sets up jQuery Ajax.
If you use @Ajax helpers in your code, like ActionLink or BeginForm, along with updating jQuery you have to update the Microsoft jQuery Unobtrusive Ajax, otherwise you can remove it.
If you remove reference to the jquery.unobtrusive-ajax.js, @Ajax helpers will be working as regular @Html helpers.
How can I know if I still use them?
Try to look for the usages of these methods.