Please use the Question Tags to state the name and full version number of the Story Format you are using, as answers can vary based on this information.
When you say "While I'm using Twine" I am going to assume you mean when you use the Test and Play options to run the (HTML) Preview of your story, and that by "I have this super handy back button" you mean the Undo (Harlowe) link or the History Backward (SugarCube) button that appears when necessary in those two story formats.
Harlowe: The Undo & Redo links should only appear in the left blank margin when their related actions are possible, this behaviour should be consisted whether you are using the Test or Play options to preview your story, or if you running the Story HTML file generated by the Publish to File option.
This story format doesn't include a built-in feature to hide the Undo & Redo links, but you can use CSS in your project's Story Stylesheet area or macros targeting the (newish) ?sidebar named hook to do this.
SugarCube: The History Backward & History Forward buttons (at the top of the left side-bar) will by default appear disabled, and will automatically enable when their related actions are possible. This functionallity should also be consistent across both preview and when running a generated story HTML file.
This story format includes a number of features that influence whether or not those buttons are displayed, like the Config.history.maxStates or Config.history.controls settings found in the Config API, and you can also use CSS you hide them.
Without seeing either a copy of your Story HTML file or knowing more about the contents of your project it is difficult to know why you're seeing the effect you are.