I will assume you are talking about the desktop release of the Twine 2.x application, you didn't state which Operating System you are running the application on some for convince sake I will assume it's a version of Windows.
That application is based on nw.js (node-webkit) which in turn is based on a custom instance of the Chromium web-browser engine. It stores all its settings (and some information about your story projects) within the Chromium web-browser's Local Storage cache, which you can access by doing the following:
WARNING: The following instructions will require you to delete some of the Twine 2 application's settings, be very careful that you only delete the indicated story format related settings because the same area also stores information about your story projects and the saves of any the stories you run using the Test or Play options. I strongly suggest you read all of the instructions first before following them.
1. Run the Twine 2 application and while looking at the Story Projects screen hold down the CTRL + ALT + SHIFT keys then press the D key to open the application's (Web) Developer Tools screen.
2. There should be a menu bar across the top of this screen, select the Application menu item to open the relevant panel. Down the left hand side should now be a list of sections, one of them should be Storage.
3. Within the Storage section select Local Storage, which should reveal a sub-item whose name starts with chrome-extension. Select this sub-item and then wait until the right hand side of the panel fills with information about the Twine 2 application. The information should consist of two columns named: Key and Value.
4. Scroll down until you find a set of Keys that start with twine-storyformats, they should be near the bottom of the list. These Keys store the information about which story formats you currently have installed.
5. You are about to delete each of the twine-storyformats related Keys one by one, you will do this by first using the mouse cursor to select one of these Keys to highlight the row, and then either press the Delete key on your keyboard or click on the small X that appears within the tool-bar above the Key column.
WARNING: You may notice a long delay in the refreshing of the list of Keys after you have deleted a Key (and its Value) or it may appear that the deletion of a Key didn't work, if this occurs then refresh the Key list before continuing with the above deletions. You can refresh the list either by moving the mouse cursor over the list and using the Right Mouse Button to display a context menu that contains a refresh item, or by using the first icon in the tool-bar above the Key column.
6. After you have delete the twine-storyformats related Keys you will need to first close the Developer Tools screen, and then close down the Twine 2 application.
7. Run the Twine 2 application again and use the Formats option to view the list of installed Story Formats, you should see that the list has been reinitialised back to it's original settings. You can now re-install any third-party or updated story formats.