You would not delete it directly from the "startup page."
You would need to find the directory where your tax returns are stored and delete them from there.
The general/default location on a windows computer would be: C:\Users\"User Name"\Documents\TurboTax where "User Name" would be relevant to your machine.
Once you navigate to that folder, you can locate and delete the files you do not need. At that point, when you restart TurboTax, the deleted files will no longer show on the "startup page."